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\section{The Algorithms}
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\label{sec:thealgorithm}
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We are going to present a novel algorithm that extends our previous work
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presented in~\cite{bkz05}.
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First we describe our previous work and in the following the new algorithm.
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To the best of our knowledge this work is the first one that becomes possible
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the construction of minimal perfect hash functions for sets in the order of
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billion of keys efficiently.
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And better, the generated functions are very compact and can be represented
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using approximately nine bits per key.
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\subsection{A Main Memory Based Algorithm}
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\subsection{An External Memory Based Algorithm}
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The idea of behind the new algorithm is the traditional divide-to-conquer approach.
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The new algorithm consists of two steps that are presented in Fig.~\ref{fig:new-algo-main-steps}:
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\begin{enumerate}
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\item Using an universal hashing function~\cite{ss89} $h_1: S \to B$ the keys from $S$ are segmented to
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a bucket set B, where $|B| = b$. We choice parameter $b$ in such way that any bucket will
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contain more than 256 keys.
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This choice is crucial to make the new algorithm works and we give details about it hereinafter.
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\item The keys in each bucket are separetaly spread into a hash table.
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\end{enumerate}
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% For two-column wide figures use
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\begin{figure}
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% Use the relevant command to insert your figure file.
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% For example, with the graphicx package use
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\centering
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\includegraphics{figs/brz.ps}
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% figure caption is below the figure
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\caption{Main steps of the new algorithm.}
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\label{fig:new-algo-main-steps}
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\end{figure}
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The main novelties are in the way the keys are segmented using external memory and spread using
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minimal perfect hash functions for each bucket. The next two sections describe each step in details.
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\subsubsection{Segmentation}
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\subsubsection{Spreading}
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% Let us show how the minimal perfect hash function~$h$
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% will be constructed.
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% We make use of three auxiliary random functions~$h_1$, $h_2$ and~$h_3:U\to V$,
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% where~$V=[0,t-1]$ for some suitably chosen integer~$t=cn$, where
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% $n=|S|$.
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% We build a random graph~$G=G(h_1,h_2)$ on~$V$,
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% whose edge set is~$\big\{\{h_1(x),h_2(x)\}:x\in S\big\}$.
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% There is an edge in~$G$ for each key in the set of keys~$S$.
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%
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% In what follows, we shall be interested in the \textit{2-core} of
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% the random graph~$G$, that is, the maximal subgraph of~$G$ with minimal
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% degree at least~$2$
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% (see, e.g., \cite{b01,jlr00}).
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% Because of its importance in our context, we call the 2-core the
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% \textit{critical} subgraph of~$G$ and denote it by~$G_\crit$.
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% The vertices and edges in~$G_\crit$ are said to be \textit{critical}.
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% We let~$V_\crit=V(G_\crit)$ and~$E_\crit=E(G_\crit)$.
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% Moreover, we let~$V_\ncrit=V-V_\crit$ be the set of {\em non-critical}
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% vertices in~$G$.
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% We also let~$V_\scrit\subseteq V_\crit$ be the set of all critical
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% vertices that have at least one non-critical vertex as a neighbour.
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% Let $E_\ncrit=E(G)-E_\crit$ be the set of {\em non-critical} edges in~$G$.
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% Finally, we let~$G_\ncrit=(V_\ncrit\cup V_\scrit,E_\ncrit)$ be the
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% {\em non-critical} subgraph of~$G$.
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% The non-critical subgraph $G_\ncrit$ corresponds to the ``acyclic part''
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% of~$G$.
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% We have $G=G_\crit\cup G_\ncrit$.
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%
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% We then construct a suitable labelling $g:V\to\ZZ$ of the vertices
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% of~$G$: we choose~$g(v)$ for each~$v\in V(G)$ in such
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% a way that~$h(x)=g(h_1(x))+g(h_2(x))$ ($x\in S$) is a
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% minimal perfect hash function for~$S$.
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% We will see later on that this labelling~$g$ can be found in linear time
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% if the number of edges in $G_\crit$ is at most $\frac{1}{2}|E(G)|$.
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%
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% Figure~\ref{prog:mainsteps} presents a pseudo code for the algorithm.
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% The procedure GenerateMPHF ($S$, $g$) receives as input the set of
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% keys~$S$ and produces the labelling~$g$.
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% The method uses a mapping, ordering and searching approach.
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% We now describe each step.
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%
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% \enlargethispage{\baselineskip}
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% \enlargethispage{\baselineskip}
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% \vspace{-11pt}
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% \begin{figure}[htb]
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% \begin{center}
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% \begin{lstlisting}[
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% ]
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% procedure @GenerateMPHF@ (@$S$@, @$g$@)
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% Mapping (@$S$@, @$G$@);
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% Ordering (@$G$@, @$G_\crit$@, @$G_\ncrit$@);
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% Searching (@$G$@, @$G_\crit$@, @$G_\ncrit$@, @$g$@);
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% \end{lstlisting}
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% \end{center}
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% \vspace{-12pt}
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% \caption{Main steps of the algorithm for constructing a minimal
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% perfect hash function}
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% \vspace{-26pt}
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% \label{prog:mainsteps}
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% \end{figure}
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%
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% \subsection{Mapping Step}
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% \label{sec:mapping}
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%
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% The procedure Mapping ($S$, $G$) receives as input the set of keys~$S$ and
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% generates the random graph $G=G(h_1,h_2)$, by generating two auxiliary
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% functions~$h_1$, $h_2:U\to[0,t-1]$.
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%
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% \def\tabela{\hbox{table}}
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% %
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% The functions~$h_1$ and~$h_2$ are constructed as follows.
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% We impose some upper bound~$L$ on the lengths of the keys in~$S$.
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% To define~$h_j$ ($j=1$,$2$), we generate an~$L\times\Sigma$ table
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% of random integers~$\tabela_j$.
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% For a key~$x\in S$ of length~$|x|\leq L$ and~$j\in\{1,2\}$, we let
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% \begin{displaymath} \nonumber
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% h_j(x) = \Big (\textstyle\sum_{i=1}^{|x|} \tabela_j[i, x[i]] \Big) \bmod t.
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% \end{displaymath}
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% The random graph~$G=G(h_1,h_2)$ has vertex set~$V=[0,t-1]$ and edge set
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% $\big\{\{h_1(x),h_2(x)\}:x\in S\big\}$. We need~$G$ to be
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% simple, i.e.,
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% $G$~should have neither loops nor multiple edges.
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% A loop occurs when $h_1(x) = h_2(x)$ for some~$x\in S$.
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% We solve this in an ad hoc manner: we simply let~$h_2(x)=(2h_1(x)+1)\bmod
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% t$ in this case.
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% If we still find a loop after this,
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% we generate another pair $(h_1,h_2)$.
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% When a multiple edge occurs we abort and generate a new pair~$(h_1,h_2)$.
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%
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% \vspace{-10pt}
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% \subsubsection{Analysis of the Mapping Step. }
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%
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% We start by discussing some facts on random graphs.
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% Let~$G=(V,E)$ with $|V|=t$ and $|E|=n$ be a random graph in the uniform
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% model~$\cG(t,n)$, the model in which all the~${{t\choose2}\choose n}$ graphs
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% on~$V$ with~$n$ edges are equiprobable.
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% The study of~$\cG(t,n)$ goes back to the classical
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% work of Erd\H os and R\'enyi~\cite{er59,er60,er61} (for a modern treatment,
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% see~\cite{b01,jlr00}).
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% Let $d=2n/t$ be the average degree of $G$.
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% It is well known that, if~$d>1$, or, equivalently,
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% if~$c<2$ (recall that we have $t=cn$),
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% then, almost every~$G$
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% contains\footnote{As is usual in the theory of random graphs, we use
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% the terms `almost every' and `almost surely' to mean `with probability
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% tending to~$1$ as~$t\to\infty$'.} a ``giant'' component of
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% order~$(1+o(1))bt$, where~$b=1-T/d$, and~$0<T<1$ is the unique solution
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% to the equation~$Te^{-T}=de^{-d}$.
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% Moreover, all the other components of~$G$ have~$O(\log t)$ vertices.
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% Also, the number of vertices in the 2-core of~$G$ (the maximal subgraph of $G$
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% with minimal degree at least~$2$) that do not belong to the giant component
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% is~$o(t)$ almost surely.
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%
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% Pittel and Wormald~\cite{pw04} present detailed results
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% for the 2-core of the giant component of the random graph~$G$.
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% Since~$\tabela_j$ ($j\in\{1,2\}$) are random, $G=G(h_1,h_2)$~is a random
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% graph.
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% In what follows, we work under the hypothesis that~$G=G(h_1,h_2)$ is drawn
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% from~$\cG(t,n)$.
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% Thus, following~\cite{pw04}, the number of vertices of~$G_\crit$ is
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% \begin{eqnarray} \label{eq:nvertices2core}
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% |V(G_\crit)| = (1+o(1))(1-T)bt
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% \end{eqnarray}
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% almost surely. Moreover, the number of edges in this 2-core is
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% \begin{eqnarray} \label{eq:nedges2core}
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% |E(G_\crit)| = (1+o(1))\Big((1-T)b+b(d+T-2)/2\Big)t \\[-4mm]\nonumber
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% \end{eqnarray}
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% almost surely.
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% Let~$d_\crit=2|E(G_\crit)|/|V(G_\crit)|$ be the average degree of~$G_\crit$.
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% We are interested in the case in which~$d_\crit$ is a constant.
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%
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% \enlargethispage{\baselineskip}
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% \enlargethispage{\baselineskip}
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% As mentioned before, for us to find
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% the labelling $g:V\to\ZZ$ of the vertices of~$G=G(h_1,h_2)$ in linear time,
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% we require that~$|E(G_\crit)|\leq\frac{1}{2}|E(G)|=\frac12|S|=n/2$.
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% The crucial step now is to determine the value
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% of~$c$ (in $t=cn$) to obtain a random graph $G=G_\crit\cup G_\ncrit$ with
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% $|E(G_\crit)|\leq\frac{1}{2}|E(G)|$.
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%
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% Table~\ref{tab:values} gives some values for~$|V(G_\crit)|$
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% and~$|E(G_\crit)|$ using Eqs~(\ref{eq:nvertices2core})
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% and~(\ref{eq:nedges2core}).
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% The theoretical value for~$c$ is around~$1.152$, which is remarkably
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% close to the empirical results presented in
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% Table~\ref{tab:probability_cve1}.
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% In this table, generated from real data, the probability $P_{|E(G_\crit)|}$
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% that $|E(G_\crit)| \le \frac{1}{2}|E(G)|$ tends to~$0$ when $c < 1.15$ and it
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% tends to $1$ when $c \ge 1.15$ and $n$ increases. We found this match between
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% the empirical and the theoretical results most pleasant,
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% and this
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% is why we consider that this random graph, conditioned on being simple,
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% strongly resembles the random graph from the uniform model~$\cG(t,n)$.
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%
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%
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% \vspace{-8pt}
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% \begin{table}[!htb]
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% {\footnotesize
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% \begin{center}
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% \begin{tabular}{|c|c|c|c|c|c|}
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% \hline
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% $d$ & $T$ & $b$ & $|V(G_\crit)|$ & $|E(G_\crit)|$ & $c$ \\
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% \hline
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% %1.730 & 0.512 & 0.704 & 0.398$n$ & 0.496$n$ & 1.156 \\
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% %1.732 & 0.511 & 0.705 & 0.398$n$ & 0.497$n$ & 1.155 \\
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% %1.733 & 0.510 & 0.706 & 0.399$n$ & 0.498$n$ & 1.154 \\
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% 1.734 & 0.510 & 0.706 & 0.399$n$ & 0.498$n$ & 1.153 \\
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% 1.736 & 0.509 & 0.707 & 0.400$n$ & 0.500$n$ & 1.152 \\
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% 1.738 & 0.508 & 0.708 & 0.401$n$ & 0.501$n$ & 1.151 \\
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% 1.739 & 0.508 & 0.708 & 0.401$n$ & 0.501$n$ & 1.150 \\
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% 1.740 & 0.507 & 0.709 & 0.401$n$ & 0.502$n$ & 1.149 \\
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% %1.742 & 0.506 & 0.709 & 0.402$n$ & 0.503$n$ & 1.148 \\
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% %1.744 & 0.505 & 0.710 & 0.403$n$ & 0.504$n$ & 1.147 \\
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% %1.746 & 0.505 & 0.711 & 0.404$n$ & 0.506$n$ & 1.145 \\
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% \hline
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% \end{tabular}
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% \end{center}
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% \caption{Determining the $c$ value theoretically}
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% \vspace{-42pt}
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% \label{tab:values}
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% }
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% \end{table}
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%
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%
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% \begin{table}
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% {\footnotesize
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% \begin{center}
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% \begin{tabular}{|c|c|c|c|c|c|c|c|}
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% \hline
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% \raisebox{-0.7em}{$c$} & \multicolumn{7}{c|}{\raisebox{-1mm}{URLs ($n$)}} \\
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% \cline{2-8}
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% & \raisebox{-1mm}{$10^3$} &\raisebox{-1mm}{$10^4$} &\raisebox{-1mm}{$10^5$} & \raisebox{-1mm}{$10^6$} & \raisebox{-1mm}{$2 \times 10^6$} & \raisebox{-1mm}{$3 \times 10^6$} & \raisebox{-1mm}{$4 \times 10^6$} \\
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% \hline
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% %1.10 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
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% %1.11 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
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% %1.12 & 0.12 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
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% 1.13 & 0.22 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
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% 1.14 & 0.35 & 0.15 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\
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% 1.15 & 0.46 & 0.55 & 0.65 & 0.87 & 0.95 & 0.97 & 1.00 \\
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% 1.16 & 0.67 & 0.90 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
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% 1.17 & 0.82 & 0.99 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
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% %1.18 & 0.91 & 0.97 & 0.98 & 1.00 & 1.00 & 1.00 & 1.00 \\
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% %1.19 & 0.94 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
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% %1.20 & 0.98 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\[1mm]
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% \hline
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% \end{tabular}
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% \end{center}
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% \caption{Probability $P_{|E_\crit|}$ that $|E(G_\crit)| \le n/2$
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% for different $c$ values and different number of keys for a collections of URLs}
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% \vspace{-25pt}
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% \label{tab:probability_cve1}
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% }
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% \end{table}
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%
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% We now briefly argue that the expected number of iterations to obtain a simple
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% graph~$G=G(h_1,h_2)$ is constant for $t=cn$ and $c=1.15$. Let~$p$ be the
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% probability of generating a random graph~$G$ without loops and without
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% multiple edges. If~$p$ is bounded from below by some positive constant, then
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% we are done, because the expected number of iterations to obtain such a graph
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% is then~$1/p=O(1)$. To estimate~$p$, we estimate the probability of
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% obtaining~$n$ \textit{distinct} objects when we independently draw $n$~objects
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% from a universe of cardinality~${t\choose2}={cn\choose2}\sim c^2n^2/2$, with
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% replacement. This latter probability is about~$e^{-{n\choose2}/{t\choose2}}$
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% for large~$n$. As~$e^{-{n\choose2}/{t\choose2}}\to e^{-1/c^2}>0$
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% as~$n\to\infty$, the expected number of iterations is~$e^{1/c^2}=2.13$ (recall
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% $c=1.15$).
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% As the expected number of iterations is $O(1)$, the mapping step takes
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% $O(n)$ time.
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%
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% \vspace{-5pt}
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% \subsection{Ordering Step}
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% \label{sec:ordering}
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%
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% The procedure Ordering ($G$, $G_\crit$, $G_\ncrit$) receives as
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% input the graph~$G$ and partitions~$G$ into the two subgraphs
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% $G_\crit$ and $G_\ncrit$, so that~$G=G_\crit\cup G_\ncrit$.
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% For that, the procedure iteratively remove all vertices of degree 1 until done.
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%
|
|
||||||
% \enlargethispage{\baselineskip}
|
|
||||||
% Figure~\ref{fig:grafordering}(a) presents a sample graph with 9 vertices
|
|
||||||
% and 8 edges, where the degree of a vertex is shown besides each vertex.
|
|
||||||
% Applying the ordering step in this graph, the $5$-vertex graph showed in
|
|
||||||
% Figure~\ref{fig:grafordering}(b) is obtained.
|
|
||||||
% All vertices with degree 0 are non-critical vertices and the others are
|
|
||||||
% critical vertices. In order to determine the vertices in $V_\scrit$ we collect all vertices
|
|
||||||
% $v \in V(G_\crit)$ with at least one vertex $u$ that is in Adj$(v)$ and
|
|
||||||
% in $V(G_\ncrit)$, as the vertex 8 in Figure~\ref{fig:grafordering}(b).
|
|
||||||
%
|
|
||||||
% \vspace{-5pt}
|
|
||||||
% \begin{figure*}[!htb]
|
|
||||||
% \begin{center}
|
|
||||||
% \scalebox{0.85}{\psfig{file=figs/grafordering.ps}}
|
|
||||||
% \end{center}
|
|
||||||
% \vspace{-10pt}
|
|
||||||
% \caption{Ordering step for a graph with 9 vertices and 8 edges}
|
|
||||||
% \vspace{-30pt}
|
|
||||||
% \label{fig:grafordering}
|
|
||||||
% \end{figure*}
|
|
||||||
%
|
|
||||||
%
|
|
||||||
% \subsubsection{Analysis of the Ordering Step. }
|
|
||||||
%
|
|
||||||
% The time complexity of the ordering step is $O(|V(G)|)$ (see \cite{chm97}).
|
|
||||||
% As $|V(G)| = t = cn$, the ordering step takes $O(n)$ time.
|
|
||||||
%
|
|
||||||
% \vspace{-5pt}
|
|
||||||
% \subsection{Searching Step}
|
|
||||||
% \label{sec:searching}
|
|
||||||
%
|
|
||||||
% In the searching step, the key part is
|
|
||||||
% the {\em perfect assignment problem}: find $g:V(G)\to\ZZ$ such that
|
|
||||||
% the function $h:E(G)\to\ZZ$ defined by
|
|
||||||
% \begin{eqnarray}
|
|
||||||
% \label{eq:phf}
|
|
||||||
% h(e) = g(a)+g(b) \qquad(e=\{a,b\})
|
|
||||||
% \end{eqnarray}
|
|
||||||
% is a bijection from~$E(G)$ to~$[0,n-1]$ (recall~$n=|S|=|E(G)|$).
|
|
||||||
% We are interested in a labelling $g:V\to\ZZ$ of
|
|
||||||
% the vertices of the graph~$G=G(h_1,h_2)$ with
|
|
||||||
% the property that if~$x$ and~$y$ are keys in~$S$, then
|
|
||||||
% $g(h_1(x))+g(h_2(x))\neq g(h_1(y))+g(h_2(y))$; that is, if we associate
|
|
||||||
% to each edge the sum of the labels on its endpoints, then these values
|
|
||||||
% should be all distinct.
|
|
||||||
% Moreover, we require that all the sums $g(h_1(x))+g(h_2(x))$ ($x\in S$)
|
|
||||||
% fall between~$0$ and~$|E(G)|-1=n-1$, so that we have a bijection
|
|
||||||
% between~$S$ and~$[0,n-1]$.
|
|
||||||
%
|
|
||||||
% The procedure Searching ($G$, $G_\crit$, $G_\ncrit$, $g$) receives
|
|
||||||
% as input~$G$, $G_\crit$, $G_\ncrit$ and finds a suitable
|
|
||||||
% $\log_2 |V(G)| + 1$ bit value for each vertex $v \in V(G)$, stored in the
|
|
||||||
% array~$g$.
|
|
||||||
% This step is first performed for the vertices in the
|
|
||||||
% critical subgraph~$G_\crit$ of $G$ (the 2-core of~$G$) and then it is
|
|
||||||
% performed for the vertices in $G_\ncrit$ (the non-critical subgraph
|
|
||||||
% of~$G$ that contains the ``acyclic part'' of $G$).
|
|
||||||
% The reason the assignment of the $g$~values is first
|
|
||||||
% performed on the vertices in~$G_\crit$ is to resolve reassignments
|
|
||||||
% as early as possible (such reassignments are consequences of the cycles
|
|
||||||
% in~$G_\crit$ and are depicted hereinafter).
|
|
||||||
%
|
|
||||||
% \vspace{-8pt}
|
|
||||||
% \subsubsection{Assignment of Values to Critical Vertices. }
|
|
||||||
% \label{sec:assignmentcv}
|
|
||||||
%
|
|
||||||
% The labels~$g(v)$ ($v\in V(G_\crit)$)
|
|
||||||
% are assigned in increasing order following a greedy
|
|
||||||
% strategy where the critical vertices~$v$ are considered one at a time,
|
|
||||||
% according to a breadth-first search on~$G_\crit$.
|
|
||||||
% If a candidate value~$x$ for~$g(v)$ is forbidden
|
|
||||||
% because setting~$g(v)=x$ would create two edges with the same sum,
|
|
||||||
% we try~$x+1$ for~$g(v)$. This fact is referred to as a {\em reassignment}.
|
|
||||||
%
|
|
||||||
% \enlargethispage{\baselineskip}
|
|
||||||
% Let $A_E$ be the set of addresses assigned to edges in $E(G_\crit)$.
|
|
||||||
% Initially $A_E = \emptyset$.
|
|
||||||
% Let $x$ be a candidate value for $g(v)$.
|
|
||||||
% Initially $x = 0$.
|
|
||||||
% Considering the subgraph $G_\crit$ in Figure~\ref{fig:grafordering}(b),
|
|
||||||
% a step by step example of the assignment of values to vertices in $G_\crit$
|
|
||||||
% is presented in Figure~\ref{fig:searching}.
|
|
||||||
% Initially, a vertex $v$ is chosen, the assignment $g(v)=x$ is made
|
|
||||||
% and $x$ is set to $x + 1$.
|
|
||||||
% For example, suppose that vertex $8$ in Figure~\ref{fig:searching}(a) is
|
|
||||||
% chosen, the assignment $g(8)=0$ is made and $x$ is set to $1$.
|
|
||||||
%
|
|
||||||
% \vspace{-12pt}
|
|
||||||
% \begin{figure*}[!htb]
|
|
||||||
% \begin{center}
|
|
||||||
% \scalebox{0.85}{\psfig{file=figs/grafsearching.ps}}
|
|
||||||
% \end{center}
|
|
||||||
% \vspace{-13pt}
|
|
||||||
% \caption{Example of the assignment of values to critical vertices}
|
|
||||||
% \vspace{-15pt}
|
|
||||||
% \label{fig:searching}
|
|
||||||
% \end{figure*}
|
|
||||||
%
|
|
||||||
% In Figure~\ref{fig:searching}(b), following the adjacency list of vertex $8$,
|
|
||||||
% the unassigned vertex $0$ is reached.
|
|
||||||
% At this point, we collect in
|
|
||||||
% the temporary variable $Y$ all adjacencies of vertex $0$ that have been assigned
|
|
||||||
% an $x$ value, and $Y = \{8\}$.
|
|
||||||
% Next, for all $u \in Y$, we check if $g(u)+x \not \in A_E$.
|
|
||||||
% Since $g(8) + 1 = 1 \not \in A_E$, then $g(0)$ is set to $1$, $x$ is incremented
|
|
||||||
% by 1 (now $x=2$) and $A_E = A_E \cup \{1\}=\{1\}$.
|
|
||||||
% Next, vertex $3$ is reached, $g(3)$ is set to $2$,
|
|
||||||
% $x$ is set to $3$ and $A_E = A_E \cup \{2\}=\{1,2\}$.
|
|
||||||
% Next, vertex $4$ is reached and $Y=\{3, 8\}$.
|
|
||||||
% Since $g(3) + 3 = 5 \not \in A_E$ and $g(8) + 3 = 3 \not \in A_E$, then
|
|
||||||
% $g(4)$ is set to $3$, $x$ is set to $4$ and $A_E = A_E \cup \{3,5\} = \{1,2,3,5\}$.
|
|
||||||
% Finally, vertex $7$ is reached and $Y=\{0, 8\}$.
|
|
||||||
% Since $g(0) + 4 = 5 \in A_E$, $x$ is incremented by 1 and set to 5, as depicted in
|
|
||||||
% Figure~\ref{fig:searching}(c).
|
|
||||||
% Since $g(8) + 5 = 5 \in A_E$, $x$ is again incremented by 1 and set to 6,
|
|
||||||
% as depicted in Figure~\ref{fig:searching}(d).
|
|
||||||
% These two reassignments are indicated by the arrows in Figure~\ref{fig:searching}.
|
|
||||||
% Since $g(0) + 6 = 7 \not \in A_E$ and $g(8) + 6 = 6 \not \in A_E$, then
|
|
||||||
% $g(7)$ is set to $6$ and $A_E = A_E \cup \{6,7\} = \{1,2,3,5,6,7\}$.
|
|
||||||
% This finishes the algorithm.
|
|
||||||
%
|
|
||||||
% \vspace{-15pt}
|
|
||||||
% \subsubsection{Assignment of Values to Non-Critical Vertices. }
|
|
||||||
% \label{sec:assignmentncv}
|
|
||||||
%
|
|
||||||
% As $G_\ncrit$ is acyclic, we can impose the order in which addresses are
|
|
||||||
% associated with edges in $G_\ncrit$, making this step simple to solve
|
|
||||||
% by a standard depth first search algorithm.
|
|
||||||
% Therefore, in the assignment of values to vertices in $G_\ncrit$ we
|
|
||||||
% benefit from the unused addresses in the gaps left by the assignment of values
|
|
||||||
% to vertices in $G_\crit$.
|
|
||||||
% For that, we start the depth-first search from the vertices in $V_\scrit$
|
|
||||||
% because the $g$ values for these critical vertices have already been assigned
|
|
||||||
% and cannot be changed.
|
|
||||||
%
|
|
||||||
% Considering the subgraph $G_\ncrit$ in Figure~\ref{fig:grafordering}(b),
|
|
||||||
% a step by step example of the assignment of values to vertices in
|
|
||||||
% $G_\ncrit$ is presented in Figure~\ref{fig:searchingncv}.
|
|
||||||
% Figure~\ref{fig:searchingncv}(a) presents the initial state of the
|
|
||||||
% algorithm.
|
|
||||||
% The critical vertex~$8$ is the only one that has non-critical
|
|
||||||
% neighbours.
|
|
||||||
% In the example presented in Figure~\ref{fig:searching}, the addresses
|
|
||||||
% $\{0, 4\}$ were not used.
|
|
||||||
% So, taking the first unused address $0$ and the vertex $1$, which is
|
|
||||||
% reached from the vertex $8$, $g(1)$ is set to
|
|
||||||
% $0 - g(8) = 0$, as shown in Figure~\ref{fig:searchingncv}(b).
|
|
||||||
% The only vertex that is reached from vertex $1$ is vertex $2$, so
|
|
||||||
% taking the unused address $4$ we set $g(2)$ to $4 - g(1) = 4$,
|
|
||||||
% as shown in Figure~\ref{fig:searchingncv}(c).
|
|
||||||
% This process is repeated until the UnAssignedAddresses list becomes empty.
|
|
||||||
%
|
|
||||||
% \vspace{-8pt}
|
|
||||||
% \begin{figure*}[!htb]
|
|
||||||
% \begin{center}
|
|
||||||
% \scalebox{0.85}{\psfig{file=figs/grafsearchingncv.ps}}
|
|
||||||
% \end{center}
|
|
||||||
% \vspace{-12pt}
|
|
||||||
% \caption{Example of the assignment of values to non-critical vertices}
|
|
||||||
% \vspace{-30pt}
|
|
||||||
% \label{fig:searchingncv}
|
|
||||||
% \end{figure*}
|
|
||||||
%
|
|
||||||
% \subsubsection{Analysis of the Searching Step. }
|
|
||||||
%
|
|
||||||
% We shall demonstrate that
|
|
||||||
% (i) the maximum value assigned to an edge is at most $n-1$ (that is, we
|
|
||||||
% generate a minimal perfect hash function), and
|
|
||||||
% (ii) the perfect assignment problem (determination of~$g$)
|
|
||||||
% can be solved in expected time $O(n)$ if the number of edges
|
|
||||||
% in $G_\crit$ is at most $\frac{1}{2}|E(G)|$.
|
|
||||||
%
|
|
||||||
% \enlargethispage{\baselineskip}
|
|
||||||
% We focus on the analysis of the assignment of values to critical vertices
|
|
||||||
% because the assignment of values to non-critical vertices
|
|
||||||
% can be solved in linear time by a depth first search algorithm.
|
|
||||||
%
|
|
||||||
% We now define certain complexity measures.
|
|
||||||
% Let $I(v)$ be the number of times a candidate value $x$ for
|
|
||||||
% $g(v)$ is incremented.
|
|
||||||
% Let $N_t$ be the total number of times that candidate values
|
|
||||||
% $x$ are incremented.
|
|
||||||
% Thus, we have~$N_t=\sum I(v)$, where the sum is over all~$v\in
|
|
||||||
% V(G_\crit)$.
|
|
||||||
%
|
|
||||||
% For simplicity, we shall suppose that $G_\crit$, the 2-core of $G$, is
|
|
||||||
% connected.\footnote{The number of vertices in~$G_\crit$ outside the giant
|
|
||||||
% component is provably very small for~$c=1.15$;
|
|
||||||
% see~\cite{b01,jlr00,pw04}.} The fact that
|
|
||||||
% every edge is either a tree edge or a back edge (see, e.g., \cite{clrs01})
|
|
||||||
% then implies the following.
|
|
||||||
%
|
|
||||||
% \begin{theorem} \label{th:nbedg}
|
|
||||||
% The number of back edges $N_\bedges$ of $G = G_\crit \cup G_\ncrit$
|
|
||||||
% is given by $N_\bedges = |E(G_\crit)| - |V(G_\crit)| + 1$.\qed
|
|
||||||
% \end{theorem}
|
|
||||||
%
|
|
||||||
% \def\maxx{{\rm max}}
|
|
||||||
% Our next result concerns the maximal value $A_\maxx$ assigned to an edge $e
|
|
||||||
% \in E(G_\crit)$ after the assignment of $g$ values to critical vertices.
|
|
||||||
%
|
|
||||||
% \begin{theorem} \label{th:Agrt}
|
|
||||||
% We have $A_\maxx\le 2|V(G_\crit)| - 3 + 2N_{t}$.
|
|
||||||
% \end{theorem}
|
|
||||||
% \vspace{-15pt}
|
|
||||||
%
|
|
||||||
% \enlargethispage{\baselineskip}
|
|
||||||
% \begin{proof}(Sketch)
|
|
||||||
% The assignment of $g$ values to critical vertices starts from 0,
|
|
||||||
% and each edge~$e$ receives the label $h(e)$
|
|
||||||
% as given by Eq.~(\ref{eq:phf}).
|
|
||||||
% The $g$ value for each vertex $v$ in $V(G_\crit)$ is assigned only once.
|
|
||||||
% A little thought shows that~$\max_v g(v)\leq |V(G_\crit)|-1+N_t$, where the
|
|
||||||
% maximum is taken over all vertices~$v$ in~$V(G_\crit)$. Moreover, two
|
|
||||||
% distinct vertices get distinct~$g$ values. Hence,
|
|
||||||
% $A_\maxx\le(|V(G_\crit)|-1+N_t)+(|V(G_\crit)|-2+N_t)
|
|
||||||
% \le2|V(G_\crit)|-3+2N_t$, as required.\qed
|
|
||||||
% \end{proof}
|
|
||||||
%
|
|
||||||
% \vspace{-15pt}
|
|
||||||
% \subsubsection{Maximal Value Assigned to an Edge. }
|
|
||||||
%
|
|
||||||
% In this section we present the following conjecture.
|
|
||||||
% \begin{conjecture} \label{conj:gretestaddr}
|
|
||||||
% For a random graph $G$ with $|E(G_\crit)|\leq n/2$ and
|
|
||||||
% $|V(G)| = 1.15n$,
|
|
||||||
% it is always possible to generate a minimal perfect hash function
|
|
||||||
% because the maximal value $A_\maxx$ assigned to an edge
|
|
||||||
% $e \in E(G_\crit)$ is at most $n - 1$.
|
|
||||||
% \end{conjecture}
|
|
||||||
%
|
|
||||||
% Let us assume for the moment that $N_{t} \le N_\bedges$.
|
|
||||||
% Then, from Theorems~\ref{th:nbedg} and~\ref{th:Agrt},
|
|
||||||
% we have
|
|
||||||
% $A_\maxx\le2|V(G_\crit)|-3+2N_t\leq2|V(G_\crit)|-3+2N_\bedges
|
|
||||||
% \leq2|V(G_\crit)|-3+2(|E(G_\crit)|-|V(G_\crit)|+1)\le2|E(G_\crit)|-1$.
|
|
||||||
% As by hypothesis $|E(G_\crit)|\leq n/2$, we have
|
|
||||||
% $A_\maxx \le n - 1$, as required.
|
|
||||||
%
|
|
||||||
% \textit{In the mathematical analysis of our algorithm, what is left
|
|
||||||
% open is a single problem:
|
|
||||||
% prove that $N_{t} \le N_\bedges$.}\footnote{%
|
|
||||||
% Bollob\'as and Pikhurko~\cite{bp04} have investigated
|
|
||||||
% a very close vertex labelling problem for random graphs.
|
|
||||||
% However, their interest was on denser random graphs, and it seems that
|
|
||||||
% different methods will have to be used to attack the sparser case that
|
|
||||||
% we are interested in here.}
|
|
||||||
%
|
|
||||||
% We now show experimental evidence that $N_{t} \le N_\bedges$.
|
|
||||||
% Considering Eqs~(\ref{eq:nvertices2core}) and~(\ref{eq:nedges2core}),
|
|
||||||
% the expected values for $|V(G_\crit)|$ and $|E(G_\crit)|$ for $c=1.15$ are
|
|
||||||
% $0.401 n$ and $0.501n$, respectively.
|
|
||||||
% From Theorem~\ref{th:nbedg},
|
|
||||||
% $N_\bedges = 0.501n - 0.401n + 1 = 0.1n + 1$.
|
|
||||||
% Table~\ref{tab:collisions1} presents the maximal value of $N_t$ obtained
|
|
||||||
% during 10,000 executions of the algorithm for different sizes of $S$.
|
|
||||||
% The maximal value of $N_t$ was always smaller than $N_\bedges = 0.1 n + 1$ and
|
|
||||||
% tends to $0.059n$ for $n\ge1{,}000{,}000$.
|
|
||||||
%
|
|
||||||
% \vspace{-5pt}
|
|
||||||
% \begin{table}[!htb]
|
|
||||||
% {\footnotesize%\small
|
|
||||||
% \begin{center}
|
|
||||||
% \begin{tabular}{|c|c|}
|
|
||||||
% \hline
|
|
||||||
% $n$ & Maximal value of $N_t$\\
|
|
||||||
% \hline
|
|
||||||
% %$1{,}000$ & $0.091 n$ \\
|
|
||||||
% $10{,}000$ & $0.067 n$ \\
|
|
||||||
% $100{,}000$ & $0.061 n$ \\
|
|
||||||
% $1{,}000{,}000$ & $0.059 n$ \\
|
|
||||||
% $2{,}000{,}000$ & $0.059 n$ \\
|
|
||||||
% %$\vdots$ & $\vdots$ \\
|
|
||||||
% \hline
|
|
||||||
% \end{tabular}
|
|
||||||
% \end{center}
|
|
||||||
% }
|
|
||||||
% \caption{The maximal value of $N_t$ for different number of URLs}
|
|
||||||
% \vspace{-40pt}
|
|
||||||
% \label{tab:collisions1}
|
|
||||||
% \end{table}
|
|
||||||
%
|
|
||||||
% \subsubsection{Time Complexity. }
|
|
||||||
% We now show that the time complexity of determining~$g(v)$
|
|
||||||
% for all critical vertices~$x\in V(G_\crit)$ is
|
|
||||||
% $O(|V(G_\crit)|)=O(n)$.
|
|
||||||
% For each unassigned vertex $v$, the adjacency list of $v$, which we
|
|
||||||
% call Adj($v$), must be traversed
|
|
||||||
% to collect the set $Y$ of adjacent vertices that have already been assigned a
|
|
||||||
% value.
|
|
||||||
% Then, for each vertex in $Y$, we check if the current candidate value $x$ is
|
|
||||||
% forbidden because setting $g(v)=x$ would create two edges with the same
|
|
||||||
% endpoint sum.
|
|
||||||
% Finally, the edge linking $v$ and $u$, for all $u \in Y$, is
|
|
||||||
% associated with
|
|
||||||
% the address that corresponds to the sum of its endpoints.
|
|
||||||
% Let $d_\crit=2|E(G_\crit)|/|V(G_\crit)|$ be the average degree of $G_\crit$,
|
|
||||||
% note that~$|Y|\leq|{\mathrm Adj}(v)|$, and suppose for simplicity
|
|
||||||
% that~$|{\mathrm Adj}(v)|=O(d_\crit)$.
|
|
||||||
% Then, putting all these together, we see that the time complexity of this
|
|
||||||
% procedure is
|
|
||||||
% \begin{eqnarray}
|
|
||||||
% &C(|V(G_\crit)|) = \sum_{v\in V(G_\crit)} \big[\:|{\mathrm Adj}(v)| +
|
|
||||||
% (I(v) \times|Y|) + |Y|\big]\nonumber\\
|
|
||||||
% &\qquad\qquad\qquad\leq\sum_{v\in V(G_\crit)}(2+I(v))|{\mathrm Adj}(v)|
|
|
||||||
% =4|E(G_\crit)|+O(N_t d_\crit).\nonumber
|
|
||||||
% \end{eqnarray}
|
|
||||||
% As $d_\crit=2\times0.501n/0.401n\simeq2.499$ (a constant) we have
|
|
||||||
% $O(|E(G_\crit)|)=O(|V(G_\crit)|)$.
|
|
||||||
% Supposing that $N_{t}\le N_\bedges$, we have, from Theorem~\ref{th:nbedg},
|
|
||||||
% that
|
|
||||||
% $
|
|
||||||
% N_{t}\le|E(G_\crit)|-|V(G_\crit)|+1
|
|
||||||
% =O(|E(G_\crit)|)$.
|
|
||||||
% We conclude that
|
|
||||||
% $C(|V(G_\crit)|)=O(|E(G_\crit)|) = O(|V(G_\crit)|)$.
|
|
||||||
% As $|V(G_\crit)| \le |V(G)|$ and $|V(G)| = cn$,
|
|
||||||
% the time required to determine~$g$ on the critical vertices is $O(n)$.
|
|
||||||
% \enlargethispage{\baselineskip}
|
|
||||||
% \vspace{-8pt}
|
|
||||||
|
|
@ -1,2 +0,0 @@
|
||||||
\section{Applications}
|
|
||||||
\label{sec:applications}
|
|
||||||
|
|
@ -1,5 +0,0 @@
|
||||||
\section{Conclusion}
|
|
||||||
|
|
||||||
% We have presented a practical method for constructing minimal perfect
|
|
||||||
% hash functions for static sets that is efficient and may be tuned
|
|
||||||
% to yield a function with a very economical description.
|
|
||||||
|
|
@ -1,178 +0,0 @@
|
||||||
\section{Experimental Results}
|
|
||||||
|
|
||||||
% We now present some experimental results.
|
|
||||||
% The same experiments were run with our algorithm and
|
|
||||||
% the algorithm due to Czech, Havas and Majewski~\cite{chm92}, referred to as
|
|
||||||
% the CHM algorithm.
|
|
||||||
% The two algorithms were implemented in the C language and
|
|
||||||
% are available at \texttt{http://cmph.sf.net}.
|
|
||||||
% Our data consists
|
|
||||||
% of a collection of 100 million
|
|
||||||
% universe resource locations (URLs) collected from the Web.
|
|
||||||
% The average length of a URL in the collection is 63 bytes.
|
|
||||||
% All experiments were carried out on
|
|
||||||
% a computer running the Linux operating system, version 2.6.7,
|
|
||||||
% with a 2.4 gigahertz processor and
|
|
||||||
% 4 gigabytes of main memory.
|
|
||||||
%
|
|
||||||
% Table~\ref{tab:characteristics} presents the main characteristics
|
|
||||||
% of the two algorithms.
|
|
||||||
% The number of edges in the graph $G=(V,E)$ is~$|S|=n$,
|
|
||||||
% the number of keys in the input set~$S$.
|
|
||||||
% The number of vertices of $G$ is equal to $1.15n$ and $2.09n$
|
|
||||||
% for our algorithm and the CHM algorithm, respectively.
|
|
||||||
% This measure is related to the amount of space to store the array $g$.
|
|
||||||
% This improves the space required to store a function in our algorithm to
|
|
||||||
% $55\%$ of the space required by the CHM algorithm.
|
|
||||||
% The number of critical edges
|
|
||||||
% is $\frac{1}{2}|E(G)|$ and 0 for our algorithm and the CHM algorithm,
|
|
||||||
% respectively.
|
|
||||||
% Our algorithm generates random graphs that contain cycles with high
|
|
||||||
% probability and the
|
|
||||||
% CHM algorithm
|
|
||||||
% generates
|
|
||||||
% acyclic random graphs.
|
|
||||||
% Finally, the CHM algorithm generates order preserving functions
|
|
||||||
% while our algorithm does not preserve order.
|
|
||||||
%
|
|
||||||
% \vspace{-10pt}
|
|
||||||
% \begin{table}[htb]
|
|
||||||
% {\footnotesize
|
|
||||||
% \begin{center}
|
|
||||||
% \begin{tabular}{|c|c|c|c|c|c|c|}
|
|
||||||
% \hline
|
|
||||||
% & $c$ & $|E(G)|$ & $|V(G)|=|g|$ & $|E(G_\crit)|$ & $G$ & Order preserving \\
|
|
||||||
% \hline
|
|
||||||
% Our algorithm & 1.15 & $n$ & $cn$ & $0.5|E(G)|$ & cyclic & no \\
|
|
||||||
% \hline
|
|
||||||
% CHM algorithm & 2.09 & $n$ & $cn$ & 0 & acyclic & yes \\
|
|
||||||
% \hline
|
|
||||||
% \end{tabular}
|
|
||||||
% \end{center}
|
|
||||||
% }
|
|
||||||
% \caption{Main characteristics of the algorithms}
|
|
||||||
% \vspace{-25pt}
|
|
||||||
% \label{tab:characteristics}
|
|
||||||
% \end{table}
|
|
||||||
%
|
|
||||||
% Table~\ref{tab:timeresults} presents time measurements.
|
|
||||||
% All times are in seconds.
|
|
||||||
% The table entries are averages over 50 trials.
|
|
||||||
% The column labelled $N_i$ gives
|
|
||||||
% the number of iterations to generate the random graph $G$
|
|
||||||
% in the mapping step of the algorithms.
|
|
||||||
% The next columns give the running times
|
|
||||||
% for the mapping plus ordering steps together and the searching
|
|
||||||
% step for each algorithm.
|
|
||||||
% The last column gives the percentage gain of our algorithm
|
|
||||||
% over the CHM algorithm.
|
|
||||||
%
|
|
||||||
% \begin{table*}
|
|
||||||
% {\footnotesize
|
|
||||||
% \begin{center}
|
|
||||||
% \begin{tabular}{|c|cccc|cccc|c|}
|
|
||||||
% \hline
|
|
||||||
% \raisebox{-0.7em}{$n$} & \multicolumn{4}{c|}{\raisebox{-1mm}{Our algorithm}} &
|
|
||||||
% \multicolumn{4}{c|}{\raisebox{-1mm}{CHM algorithm}}& \raisebox{-0.2em}{Gain}\\
|
|
||||||
% \cline{2-5} \cline{6-9}
|
|
||||||
% & \raisebox{-1mm}{$N_i$} &\raisebox{-1mm}{Map+Ord} &
|
|
||||||
% \raisebox{-1mm}{Search} &\raisebox{-1mm}{Total} &
|
|
||||||
% \raisebox{-1mm}{$N_i$} &\raisebox{-1mm}{Map+Ord} &\raisebox{-1mm}{Search} &
|
|
||||||
% \raisebox{-1mm}{Total} & \raisebox{0.2em}{(\%)}\\
|
|
||||||
% \hline
|
|
||||||
% %1,562,500 & 2.28 & 8.54 & 2.37 & 10.91 & 2.70 & 14.56 & 1.57 & 16.13 & 48 \\ %[1mm]
|
|
||||||
% %3,125,000 & 2.16 & 15.92 & 4.88 & 20.80 & 2.85 & 30.36 & 3.20 & 33.56 & 61 \\ %[1mm]
|
|
||||||
% 6,250,000 & 2.20 & 33.09 & 10.48 & 43.57 & 2.90 & 62.26 & 6.76 & 69.02 & 58 \\ %[1mm]
|
|
||||||
% 12,500,000 & 2.00 & 63.26 & 23.04 & 86.30 & 2.60 & 117.99 & 14.94 & 132.92 & 54 \\ %[1mm]
|
|
||||||
% 25,000,000 & 2.00 & 130.79 & 51.55 & 182.34 & 2.80 & 262.05 & 33.68 & 295.73 & 62 \\ %[1mm]
|
|
||||||
% %50,000,000 & 2.07 & 273.75 & 114.12 & 387.87 & 2.90 & 577.59 & 73.97 & 651.56 & 68 \\ %[1mm]
|
|
||||||
% 100,000,000 & 2.07 & 567.47 & 243.13 & 810.60 & 2.80 & 1,131.06 & 157.23 & 1,288.29 & 59 \\ %[1mm]
|
|
||||||
% \hline
|
|
||||||
% \end{tabular}
|
|
||||||
% \end{center}
|
|
||||||
% \caption{Time measurements
|
|
||||||
% for our algorithm and the CHM algorithm}
|
|
||||||
% \vspace{-25pt}
|
|
||||||
% \label{tab:timeresults}
|
|
||||||
% }\end{table*}
|
|
||||||
%
|
|
||||||
% \enlargethispage{\baselineskip}
|
|
||||||
% The mapping step of the new algorithm is faster because
|
|
||||||
% the expected number of iterations in the mapping step to generate
|
|
||||||
% $G$ are 2.13 and 2.92 for our algorithm and the CHM algorithm, respectively.
|
|
||||||
% The graph $G$ generated by our algorithm
|
|
||||||
% has $1.15n$ vertices, against $2.09n$ for the CHM algorithm.
|
|
||||||
% These two facts make our algorithm faster in the mapping step.
|
|
||||||
% The ordering step of our algorithm is approximately equal to
|
|
||||||
% the time to check if $G$ is acyclic for the CHM algorithm.
|
|
||||||
% The searching step of the CHM algorithm is faster, but the total
|
|
||||||
% time of our algorithm is, on average, approximately 58\% faster
|
|
||||||
% than the CHM algorithm.
|
|
||||||
%
|
|
||||||
% The experimental results fully backs the theoretical results.
|
|
||||||
% It is important to notice the times for the searching step:
|
|
||||||
% for both algorithms they are not the dominant times,
|
|
||||||
% and the experimental results clearly show
|
|
||||||
% a linear behavior for the searching step.
|
|
||||||
%
|
|
||||||
% We now present a heuristic that reduces the space requirement
|
|
||||||
% to any given value between $1.15n$ words and $0.93n$ words.
|
|
||||||
% The heuristic reuses, when possible, the set
|
|
||||||
% of $x$ values that caused reassignments, just before trying $x+1$
|
|
||||||
% (see Section~\ref{sec:searching}).
|
|
||||||
% The lower limit $c=0.93$ was obtained experimentally.
|
|
||||||
% We generate $10{,}000$ random graphs for
|
|
||||||
% each size $n$ ($n=10^5$, $5 \times 10^5$, $10^6$, $2\times 10^6$).
|
|
||||||
% With $c=0.93$ we were always able to generate~$h$, but with $c=0.92$ we never
|
|
||||||
% succeeded.
|
|
||||||
% Decreasing the value of $c$ leads to an increase in the number of
|
|
||||||
% iterations to generate $G$.
|
|
||||||
% For example, for $c=1$ and $c=0.93$, the analytical expected number
|
|
||||||
% of iterations are $2.72$ and $3.17$, respectively
|
|
||||||
% (for $n=12{,}500{,}000$, the number of iterations are 2.78 for $c=1$ and 3.04
|
|
||||||
% for $c=0.93$).
|
|
||||||
% Table~\ref{tab:timeresults2} presents the total times to construct a
|
|
||||||
% function for $n=12{,}500{,}000$, with an increase from $86.31$ seconds
|
|
||||||
% for $c=1.15$ (see Table~\ref{tab:timeresults}) to
|
|
||||||
% $101.74$ seconds for $c=1$ and to $102.19$ seconds for $c=0.93$.
|
|
||||||
%
|
|
||||||
% \vspace{-5pt}
|
|
||||||
% \begin{table*}
|
|
||||||
% {\footnotesize
|
|
||||||
% \begin{center}
|
|
||||||
% \begin{tabular}{|c|cccc|cccc|}
|
|
||||||
% \hline
|
|
||||||
% \raisebox{-0.7em}{$n$} & \multicolumn{4}{c|}{\raisebox{-1mm}{Our algorithm $c=1.00$}} &
|
|
||||||
% \multicolumn{4}{c|}{\raisebox{-1mm}{Our algorithm $c=0.93$}} \\
|
|
||||||
% \cline{2-5} \cline{6-9}
|
|
||||||
% & \raisebox{-1mm}{$N_i$} &\raisebox{-1mm}{Map+Ord} &
|
|
||||||
% \raisebox{-1mm}{Search} &\raisebox{-1mm}{Total} &
|
|
||||||
% \raisebox{-1mm}{$N_i$} &\raisebox{-1mm}{Map+Ord} &\raisebox{-1mm}{Search} &
|
|
||||||
% \raisebox{-1mm}{Total} \\%[0.3mm]
|
|
||||||
% \hline%\\[-2mm]
|
|
||||||
% 12,500,000 & 2.78 & 76.68 & 25.06 & 101.74 & 3.04 & 76.39 & 25.80 & 102.19 \\ %[1mm]
|
|
||||||
% \hline
|
|
||||||
% \end{tabular}
|
|
||||||
% \end{center}
|
|
||||||
% \caption{Time measurements
|
|
||||||
% for our tuned algorithm with $c=1.00$ and $c=0.93$}
|
|
||||||
% \vspace{-25pt}
|
|
||||||
% \label{tab:timeresults2}
|
|
||||||
% }
|
|
||||||
% \end{table*}
|
|
||||||
%
|
|
||||||
% We compared our algorithm with the ones proposed by Pagh~\cite{p99} and
|
|
||||||
% Dietzfelbinger and Hagerup~\cite{dh01}, respectively. The authors sent to us their
|
|
||||||
% source code. In their implementation the set of keys is a set of random integers.
|
|
||||||
% We modified our implementation to generate our~$h$ from a set of random
|
|
||||||
% integers in order to make a fair comparison. For a set of $10^6$ random integers,
|
|
||||||
% the times to generate a minimal perfect hash function were $2.7 s$, $4 s$ and $4.5 s$ for
|
|
||||||
% our algorithm, Pagh's algorithm and Dietzfelbinger and Hagerup's algorithm, respectively.
|
|
||||||
% Thus, our algorithm was 48\% faster than Pagh's algorithm and 67\% faster than
|
|
||||||
% Dietzfelbinger and Hagerup's algorithm, on average. This gain was maintained for sets with different
|
|
||||||
% sizes.
|
|
||||||
% Our algorithm needs $kn$ ($k \in [0.93, 1.15]$) words to store
|
|
||||||
% the resulting function, while Pagh's algorithm needs $kn$ ($k > 2$) words and
|
|
||||||
% Dietzfelbinger and Hagerup's algorithm needs $kn$ ($k \in [1.13, 1.15]$) words.
|
|
||||||
% The time to generate the functions is inversely proportional to the value of $k$.
|
|
||||||
% \enlargethispage{\baselineskip}
|
|
||||||
|
|
@ -1,135 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 32 #bebebe
|
|
||||||
6 3285 3600 3555 4230
|
|
||||||
6 3285 3780 3555 4230
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3285 4140 3555 4140 3555 4230 3285 4230 3285 4140
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3285 4050 3555 4050 3555 4140 3285 4140 3285 4050
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3285 3960 3555 3960 3555 4050 3285 4050 3285 3960
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3285 3870 3555 3870 3555 3960 3285 3960 3285 3870
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3285 3780 3555 3780 3555 3870 3285 3870 3285 3780
|
|
||||||
-6
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3285 3690 3555 3690 3555 3780 3285 3780 3285 3690
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3285 3600 3555 3600 3555 3690 3285 3690 3285 3600
|
|
||||||
-6
|
|
||||||
6 1800 4500 3330 5175
|
|
||||||
2 3 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 8
|
|
||||||
1800 4770 2070 4770 2070 4500 3060 4500 3060 4770 3330 4770
|
|
||||||
2565 5175 1800 4770
|
|
||||||
4 0 0 50 -1 0 10 0.0000 4 150 600 2265 4867 Spreading\001
|
|
||||||
-6
|
|
||||||
6 2250 3060 2880 3600
|
|
||||||
6 2250 3060 2880 3600
|
|
||||||
6 2250 3060 2880 3600
|
|
||||||
6 2250 3060 2880 3600
|
|
||||||
2 3 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 8
|
|
||||||
2250 3330 2430 3330 2430 3060 2700 3060 2700 3330 2880 3330
|
|
||||||
2565 3600 2250 3330
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 10 0.0000 4 105 75 2521 3382 h\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 6 0.0000 4 60 45 2589 3419 1\001
|
|
||||||
-6
|
|
||||||
6 1395 2655 3825 2970
|
|
||||||
2 4 0 1 0 7 50 -1 -1 0.000 0 0 7 0 0 5
|
|
||||||
3825 2970 3825 2655 1395 2655 1395 2970 3825 2970
|
|
||||||
4 0 0 50 -1 0 10 0.0000 4 135 795 2212 2850 Set of Keys S\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1395 4230 3825 4230
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1395 4140 1665 4140 1665 4230 1395 4230 1395 4140
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1395 4050 1665 4050 1665 4140 1395 4140 1395 4050
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1665 4140 1935 4140 1935 4230 1665 4230 1665 4140
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1665 4050 1935 4050 1935 4140 1665 4140 1665 4050
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1665 3960 1935 3960 1935 4050 1665 4050 1665 3960
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1665 3870 1935 3870 1935 3960 1665 3960 1665 3870
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1665 3780 1935 3780 1935 3870 1665 3870 1665 3780
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
2205 4140 2475 4140 2475 4230 2205 4230 2205 4140
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
2205 4050 2475 4050 2475 4140 2205 4140 2205 4050
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
2205 3960 2475 3960 2475 4050 2205 4050 2205 3960
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
2205 3870 2475 3870 2475 3960 2205 3960 2205 3870
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1665 3690 1935 3690 1935 3780 1665 3780 1665 3690
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
2745 4140 3015 4140 3015 4230 2745 4230 2745 4140
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3015 4140 3285 4140 3285 4230 3015 4230 3015 4140
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
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|
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cp gs col0 s gr
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|
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cp gs col0 s gr
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cp gs col0 s gr
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|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2745 3870 m 3015 3870 l 3015 3960 l 2745 3960 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2745 3780 m 3015 3780 l 3015 3870 l 2745 3870 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1260 5400 m
|
|
||||||
4230 5400 l gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1530 5310 m 1800 5310 l 1800 5400 l 1530 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2070 5310 m 2340 5310 l 2340 5400 l 2070 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2340 5310 m 2610 5310 l 2610 5400 l 2340 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2610 5310 m 2880 5310 l 2880 5400 l 2610 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2880 5310 m 3150 5310 l 3150 5400 l 2880 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3420 5310 m 3690 5310 l 3690 5400 l 3420 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3690 5310 m 3960 5310 l 3960 5400 l 3690 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3960 5310 m 4230 5310 l 4230 5400 l 3960 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1800 5310 m 2070 5310 l 2070 5400 l 1800 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3150 5310 m 3420 5310 l 3420 5400 l 3150 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1260 5310 m 1530 5310 l 1530 5400 l 1260 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3510 m 3555 3510 l 3555 3600 l 3285 3600 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3420 m 3555 3420 l 3555 3510 l 3285 3510 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
1485 4410 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
3600 4410 m
|
|
||||||
gs 1 -1 sc (b-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
720 4050 m
|
|
||||||
gs 1 -1 sc (Buckets) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
900 4230 m
|
|
||||||
gs 1 -1 sc (B) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
4005 5580 m
|
|
||||||
gs 1 -1 sc (n-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
1350 5580 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
450 5400 m
|
|
||||||
gs 1 -1 sc (Hash Table) col0 sh gr
|
|
||||||
% here ends figure;
|
|
||||||
$F2psEnd
|
|
||||||
rs
|
|
||||||
showpage
|
|
||||||
%%Trailer
|
|
||||||
%EOF
|
|
||||||
|
|
@ -1,206 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
6 2340 2970 4095 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3892.500 2047.500 2835 3825 3105 3960 3375 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 2677.500 3802.500 3330 3555 3375 3825 3330 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3523.500 4635.900 3375 4095 3060 4320 2970 4545
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3802.500 4567.500 3465 4050 3690 3960 3915 3960
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3686.786 4181.786 3915 4005 3960 4275 3780 4455
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3127.500 3802.500 3285 3555 2970 3555 2835 3825
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3127.500 4432.500 3375 4140 3510 4410 3420 4680
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3220.500 4507.500 2970 4590 3195 4770 3420 4680
|
|
||||||
6 3825 3870 4050 4095
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3937 3982 94 92 3937 3982 3980 4067
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3900 4035 2\001
|
|
||||||
-6
|
|
||||||
6 3330 4545 3555 4770
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3442 4657 94 92 3442 4657 3485 4742
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3405 4710 4\001
|
|
||||||
-6
|
|
||||||
6 2880 4455 3105 4680
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 2992 4567 94 92 2992 4567 3035 4652
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 2955 4620 5\001
|
|
||||||
-6
|
|
||||||
6 2745 3690 2970 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 2857 3802 94 92 2857 3802 2900 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 2820 3855 7\001
|
|
||||||
-6
|
|
||||||
6 3195 3420 3420 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3307 3532 94 92 3307 3532 3350 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3270 3585 0\001
|
|
||||||
-6
|
|
||||||
6 3285 3960 3510 4185
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3397 4072 94 92 3397 4072 3440 4157
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3360 4125 8\001
|
|
||||||
-6
|
|
||||||
6 2655 4050 2880 4275
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 2767 4162 94 92 2767 4162 2810 4247
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 2730 4215 6\001
|
|
||||||
-6
|
|
||||||
6 3600 3510 3825 3735
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 3712 3622 94 92 3712 3622 3755 3707
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3675 3675 1\001
|
|
||||||
-6
|
|
||||||
6 3690 4320 3915 4545
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 3802 4432 94 92 3802 4432 3845 4517
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3765 4485 3\001
|
|
||||||
-6
|
|
||||||
6 3285 2970 3465 3150
|
|
||||||
2 2 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 5
|
|
||||||
3285 2970 3465 2970 3465 3150 3285 3150 3285 2970
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3337 3112 2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3645 3465 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 2430 4230 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 2655 4635 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3330 4905 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 2520 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3735 4680 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3870 3825 d:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3510 4185 d:5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3240 3375 d:2\001
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 135 105 3060 3105 Q\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 2340 3105 b)\001
|
|
||||||
-6
|
|
||||||
6 450 2970 2115 4905
|
|
||||||
6 450 3240 2115 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1912.500 2047.500 855 3825 1125 3960 1395 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 697.500 3802.500 1350 3555 1395 3825 1350 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1543.500 4635.900 1395 4095 1080 4320 990 4545
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1822.500 4567.500 1485 4050 1710 3960 1935 3960
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1706.786 4181.786 1935 4005 1980 4275 1800 4455
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1147.500 3802.500 1305 3555 990 3555 855 3825
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1147.500 4432.500 1395 4140 1530 4410 1440 4680
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1240.500 4507.500 990 4590 1215 4770 1440 4680
|
|
||||||
6 1845 3870 2070 4095
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1957 3982 94 92 1957 3982 2000 4067
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1920 4035 2\001
|
|
||||||
-6
|
|
||||||
6 1710 4320 1935 4545
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1822 4432 94 92 1822 4432 1865 4517
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1785 4485 3\001
|
|
||||||
-6
|
|
||||||
6 1350 4545 1575 4770
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1462 4657 94 92 1462 4657 1505 4742
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1425 4710 4\001
|
|
||||||
-6
|
|
||||||
6 900 4455 1125 4680
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1012 4567 94 92 1012 4567 1055 4652
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 975 4620 5\001
|
|
||||||
-6
|
|
||||||
6 765 3690 990 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 877 3802 94 92 877 3802 920 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 840 3855 7\001
|
|
||||||
-6
|
|
||||||
6 1215 3420 1440 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1327 3532 94 92 1327 3532 1370 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1290 3585 0\001
|
|
||||||
-6
|
|
||||||
6 1305 3960 1530 4185
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1417 4072 94 92 1417 4072 1460 4157
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1380 4125 8\001
|
|
||||||
-6
|
|
||||||
6 675 4050 900 4275
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 787 4162 94 92 787 4162 830 4247
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 750 4215 6\001
|
|
||||||
-6
|
|
||||||
6 1620 3510 1845 3735
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 1732 3622 94 92 1732 3622 1775 3707
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1695 3675 1\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1665 3465 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 450 4230 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 675 4635 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1350 4905 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 540 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1755 4680 d:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1890 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1530 4185 d:5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1260 3375 d:2\001
|
|
||||||
-6
|
|
||||||
6 1080 2970 1485 3150
|
|
||||||
6 1305 2970 1485 3150
|
|
||||||
2 2 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 5
|
|
||||||
1305 2970 1485 2970 1485 3150 1305 3150 1305 2970
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1357 3112 3\001
|
|
||||||
-6
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 135 105 1080 3105 Q\001
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
6 4320 2970 6075 4905
|
|
||||||
6 4410 3015 6075 4905
|
|
||||||
6 5085 3015 5360 3156
|
|
||||||
6 5225 3015 5360 3150
|
|
||||||
1 1 0 1 0 33 45 -1 40 0.000 1 0.0000 5312 3080 44 52 5312 3080 5334 3125
|
|
||||||
2 1 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 2
|
|
||||||
5330 3020 5293 3141
|
|
||||||
-6
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 135 105 5085 3126 Q\001
|
|
||||||
-6
|
|
||||||
6 4410 3240 6075 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5872.500 2047.500 4815 3825 5085 3960 5355 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4657.500 3802.500 5310 3555 5355 3825 5310 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5503.500 4635.900 5355 4095 5040 4320 4950 4545
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5782.500 4567.500 5445 4050 5670 3960 5895 3960
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5666.786 4181.786 5895 4005 5940 4275 5760 4455
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5107.500 3802.500 5265 3555 4950 3555 4815 3825
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5107.500 4432.500 5355 4140 5490 4410 5400 4680
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5200.500 4507.500 4950 4590 5175 4770 5400 4680
|
|
||||||
6 5310 4545 5535 4770
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5422 4657 94 92 5422 4657 5465 4742
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5385 4710 4\001
|
|
||||||
-6
|
|
||||||
6 4860 4455 5085 4680
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4972 4567 94 92 4972 4567 5015 4652
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4935 4620 5\001
|
|
||||||
-6
|
|
||||||
6 4725 3690 4950 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4837 3802 94 92 4837 3802 4880 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4800 3855 7\001
|
|
||||||
-6
|
|
||||||
6 5175 3420 5400 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5287 3532 94 92 5287 3532 5330 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5250 3585 0\001
|
|
||||||
-6
|
|
||||||
6 5265 3960 5490 4185
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5377 4072 94 92 5377 4072 5420 4157
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5340 4125 8\001
|
|
||||||
-6
|
|
||||||
6 4635 4050 4860 4275
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 4747 4162 94 92 4747 4162 4790 4247
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4710 4215 6\001
|
|
||||||
-6
|
|
||||||
6 5580 3510 5805 3735
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 5692 3622 94 92 5692 3622 5735 3707
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5655 3675 1\001
|
|
||||||
-6
|
|
||||||
6 5670 4320 5895 4545
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 5782 4432 94 92 5782 4432 5825 4517
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5745 4485 3\001
|
|
||||||
-6
|
|
||||||
6 5805 3870 6030 4095
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 5917 3982 94 92 5917 3982 5960 4067
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5880 4035 2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5625 3465 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 4410 4230 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 4635 4635 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5310 4905 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 4500 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5715 4680 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5850 3825 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5490 4185 d:4\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5220 3375 d:2\001
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 3105 c)\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 360 3105 a)\001
|
|
||||||
|
|
@ -1,219 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
6 270 5220 1980 6615
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 855 5400 1080 5355 1305 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 967.500 5962.500 1620 5715 1665 5940 1620 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 1305 6480 1080 6525 855 6480
|
|
||||||
6 450 5625 630 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 5715 90 90 540 5715 630 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 510 5752 6\001
|
|
||||||
-6
|
|
||||||
6 765 5310 945 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 5400 90 90 855 5400 945 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 825 5437 7\001
|
|
||||||
-6
|
|
||||||
6 1215 5310 1395 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 5400 90 90 1305 5400 1395 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1275 5437 0\001
|
|
||||||
-6
|
|
||||||
6 1530 5625 1710 5805
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 5715 90 90 1620 5715 1710 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1590 5752 1\001
|
|
||||||
-6
|
|
||||||
6 1530 6075 1710 6255
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 6165 90 90 1620 6165 1710 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1590 6202 2\001
|
|
||||||
-6
|
|
||||||
6 1215 6390 1395 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 6480 90 90 1305 6480 1395 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1275 6517 3\001
|
|
||||||
-6
|
|
||||||
6 765 6390 945 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 6480 90 90 855 6480 945 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 825 6517 4\001
|
|
||||||
-6
|
|
||||||
6 450 6075 630 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 6165 90 90 540 6165 630 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 510 6202 5\001
|
|
||||||
-6
|
|
||||||
6 990 5850 1170 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1080 5940 90 90 1080 5940 1170 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1050 5977 8\001
|
|
||||||
-6
|
|
||||||
6 1665 5310 1980 5490
|
|
||||||
6 1800 5310 1980 5490
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1800 5310 1980 5310 1980 5490 1800 5490 1800 5310
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 1860 5437 2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 90 1665 5445 Q\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1620 5715
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 630 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 810 5985 d:5\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1395 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1755 5670 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1755 6255 d:1\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1440 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 585 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 270 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 270 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 270 5355 a)\001
|
|
||||||
-6
|
|
||||||
6 4410 5220 6120 6615
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5220.000 5940.000 4995 5400 5220 5355 5445 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5107.500 5962.500 5760 5715 5805 5940 5760 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5220.000 5940.000 5445 6480 5220 6525 4995 6480
|
|
||||||
6 4590 5625 4770 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 5715 90 90 4680 5715 4770 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 5752 6\001
|
|
||||||
-6
|
|
||||||
6 4905 5310 5085 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4995 5400 90 90 4995 5400 5085 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4965 5437 7\001
|
|
||||||
-6
|
|
||||||
6 5355 5310 5535 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5445 5400 90 90 5445 5400 5535 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5415 5437 0\001
|
|
||||||
-6
|
|
||||||
6 5355 6390 5535 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5445 6480 90 90 5445 6480 5535 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5415 6517 3\001
|
|
||||||
-6
|
|
||||||
6 4905 6390 5085 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4995 6480 90 90 4995 6480 5085 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4965 6517 4\001
|
|
||||||
-6
|
|
||||||
6 4590 6075 4770 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 6165 90 90 4680 6165 4770 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 6202 5\001
|
|
||||||
-6
|
|
||||||
6 5130 5850 5310 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5220 5940 90 90 5220 5940 5310 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5190 5977 8\001
|
|
||||||
-6
|
|
||||||
6 5670 6075 5850 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 6165 90 90 5760 6165 5850 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 6202 2\001
|
|
||||||
-6
|
|
||||||
6 5670 5625 5850 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 5715 90 90 5760 5715 5850 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 5752 1\001
|
|
||||||
-6
|
|
||||||
6 5965 5332 6100 5467
|
|
||||||
1 1 0 1 0 33 45 -1 40 0.000 1 0.0000 6052 5397 44 52 6052 5397 6074 5442
|
|
||||||
2 1 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 2
|
|
||||||
6070 5337 6033 5458
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 5445 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 4995 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 5445 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 4995 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 5760 5715
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5221 5943 5761 5718
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4770 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4950 5985 d:4\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5535 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5895 5670 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5895 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5580 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4725 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4410 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4410 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4410 5355 c)\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 90 5850 5445 Q\001
|
|
||||||
-6
|
|
||||||
6 2340 5220 4050 6615
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 2925 5400 3150 5355 3375 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3037.500 5962.500 3690 5715 3735 5940 3690 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 3375 6480 3150 6525 2925 6480
|
|
||||||
6 2520 5625 2700 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 5715 90 90 2610 5715 2700 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2580 5752 6\001
|
|
||||||
-6
|
|
||||||
6 2835 5310 3015 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 5400 90 90 2925 5400 3015 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2895 5437 7\001
|
|
||||||
-6
|
|
||||||
6 3285 5310 3465 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 5400 90 90 3375 5400 3465 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3345 5437 0\001
|
|
||||||
-6
|
|
||||||
6 3285 6390 3465 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 6480 90 90 3375 6480 3465 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3345 6517 3\001
|
|
||||||
-6
|
|
||||||
6 2835 6390 3015 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 6480 90 90 2925 6480 3015 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2895 6517 4\001
|
|
||||||
-6
|
|
||||||
6 2520 6075 2700 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 6165 90 90 2610 6165 2700 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2580 6202 5\001
|
|
||||||
-6
|
|
||||||
6 3060 5850 3240 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3150 5940 90 90 3150 5940 3240 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3120 5977 8\001
|
|
||||||
-6
|
|
||||||
6 3735 5310 4050 5490
|
|
||||||
6 3870 5310 4050 5490
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3870 5310 4050 5310 4050 5490 3870 5490 3870 5310
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 3930 5437 1\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 90 3735 5445 Q\001
|
|
||||||
-6
|
|
||||||
6 3600 5625 3780 5805
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3690 5715 90 90 3690 5715 3780 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3660 5752 1\001
|
|
||||||
-6
|
|
||||||
6 3600 6075 3780 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3690 6165 90 90 3690 6165 3780 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3660 6202 2\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3690 5715
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3151 5943 3691 5718
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2700 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2880 5985 d:5\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3465 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3825 5670 d:1\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3825 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3510 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2655 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2340 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2340 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 2340 5355 b)\001
|
|
||||||
-6
|
|
||||||
|
|
@ -1,130 +0,0 @@
|
||||||
#FIG 3.2
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d6d3d6
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 855 5400 1080 5355 1305 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 967.500 5962.500 1620 5715 1665 5940 1620 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 1305 6480 1080 6525 855 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 2925 5400 3150 5355 3375 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3037.500 5962.500 3690 5715 3735 5940 3690 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 3375 6480 3150 6525 2925 6480
|
|
||||||
6 450 5625 630 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 5715 90 90 540 5715 630 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 510 5752 6\001
|
|
||||||
-6
|
|
||||||
6 765 5310 945 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 5400 90 90 855 5400 945 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 825 5437 7\001
|
|
||||||
-6
|
|
||||||
6 1215 5310 1395 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 5400 90 90 1305 5400 1395 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1275 5437 0\001
|
|
||||||
-6
|
|
||||||
6 1530 5625 1710 5805
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 5715 90 90 1620 5715 1710 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1590 5752 1\001
|
|
||||||
-6
|
|
||||||
6 1530 6075 1710 6255
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 6165 90 90 1620 6165 1710 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1590 6202 2\001
|
|
||||||
-6
|
|
||||||
6 1215 6390 1395 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 6480 90 90 1305 6480 1395 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1275 6517 3\001
|
|
||||||
-6
|
|
||||||
6 765 6390 945 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 6480 90 90 855 6480 945 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 825 6517 4\001
|
|
||||||
-6
|
|
||||||
6 450 6075 630 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 6165 90 90 540 6165 630 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 510 6202 5\001
|
|
||||||
-6
|
|
||||||
6 990 5850 1170 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1080 5940 90 90 1080 5940 1170 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1050 5977 8\001
|
|
||||||
-6
|
|
||||||
6 2520 5625 2700 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 5715 90 90 2610 5715 2700 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2580 5752 6\001
|
|
||||||
-6
|
|
||||||
6 2835 5310 3015 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 5400 90 90 2925 5400 3015 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2895 5437 7\001
|
|
||||||
-6
|
|
||||||
6 3285 5310 3465 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 5400 90 90 3375 5400 3465 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3345 5437 0\001
|
|
||||||
-6
|
|
||||||
6 3285 6390 3465 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 6480 90 90 3375 6480 3465 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3345 6517 3\001
|
|
||||||
-6
|
|
||||||
6 2835 6390 3015 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 6480 90 90 2925 6480 3015 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2895 6517 4\001
|
|
||||||
-6
|
|
||||||
6 2520 6075 2700 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 6165 90 90 2610 6165 2700 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2580 6202 5\001
|
|
||||||
-6
|
|
||||||
6 3060 5850 3240 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3150 5940 90 90 3150 5940 3240 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3120 5977 8\001
|
|
||||||
-6
|
|
||||||
6 3600 6075 3780 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3690 6165 90 90 3690 6165 3780 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3660 6202 2\001
|
|
||||||
-6
|
|
||||||
6 3600 5625 3780 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3690 5715 90 90 3690 5715 3780 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3660 5752 1\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1620 5715
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3690 5715
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3151 5943 3691 5718
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 630 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 810 5985 d:5\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1395 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1755 5670 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1755 6255 d:1\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1440 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 585 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 270 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 270 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 150 135 270 5355 a)\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2700 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2880 5985 d:4\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3465 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3825 5670 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3825 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3510 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2655 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2340 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2340 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 150 150 2340 5355 b)\001
|
|
||||||
|
|
@ -1,168 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5692.500 1777.500 4635 3555 4905 3690 5175 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4477.500 3532.500 5130 3285 5175 3555 5130 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5323.500 4365.900 5175 3825 4860 4050 4770 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 4927.500 3532.500 5085 3285 4770 3285 4635 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4927.500 4162.500 5175 3870 5310 4140 5220 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5020.500 4237.500 4770 4320 4995 4500 5220 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 10012.500 1777.500 8955 3555 9225 3690 9495 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 8797.500 3532.500 9450 3285 9495 3555 9450 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 9643.500 4365.900 9495 3825 9180 4050 9090 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 9247.500 3532.500 9405 3285 9090 3285 8955 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 9247.500 4162.500 9495 3870 9630 4140 9540 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 9340.500 4237.500 9090 4320 9315 4500 9540 4410
|
|
||||||
6 5130 4275 5355 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5242 4387 94 92 5242 4387 5285 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5205 4440 4\001
|
|
||||||
-6
|
|
||||||
6 4680 4185 4905 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4792 4297 94 92 4792 4297 4835 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4755 4350 5\001
|
|
||||||
-6
|
|
||||||
6 4545 3420 4770 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4657 3532 94 92 4657 3532 4700 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4620 3585 7\001
|
|
||||||
-6
|
|
||||||
6 5085 3690 5310 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5197 3802 94 92 5197 3802 5240 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5160 3855 8\001
|
|
||||||
-6
|
|
||||||
6 4995 3150 5220 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5107 3262 94 92 5107 3262 5150 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5070 3315 0\001
|
|
||||||
-6
|
|
||||||
6 7200 2970 8460 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 8572.500 1777.500 7515 3555 7785 3690 8055 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7357.500 3532.500 8010 3285 8055 3555 8010 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 8203.500 4365.900 8055 3825 7740 4050 7650 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 7807.500 3532.500 7965 3285 7650 3285 7515 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7807.500 4162.500 8055 3870 8190 4140 8100 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 7900.500 4237.500 7650 4320 7875 4500 8100 4410
|
|
||||||
6 7560 4185 7785 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 7672 4297 94 92 7672 4297 7715 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 7635 4350 5\001
|
|
||||||
-6
|
|
||||||
6 7425 3420 7650 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 7537 3532 94 92 7537 3532 7580 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 7500 3585 7\001
|
|
||||||
-6
|
|
||||||
6 7875 3150 8100 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 7987 3262 94 92 7987 3262 8030 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 7950 3315 0\001
|
|
||||||
-6
|
|
||||||
6 7965 3690 8190 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 8077 3802 94 92 8077 3802 8120 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 8040 3855 8\001
|
|
||||||
-6
|
|
||||||
6 8010 4275 8235 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 8122 4387 94 92 8122 4387 8165 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 8085 4440 4\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7553 4891 7733 4666
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7560 3825 7785 3645
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 7335 4365 g:3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 7200 3555 g:5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 7920 3105 g:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7560 3240 6\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7785 3645 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 8100 3555 1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 8235 4185 2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7740 4635 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7650 4005 3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8235 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8010 4635 g:2\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 7200 3105 c)\001
|
|
||||||
-6
|
|
||||||
6 9000 4185 9225 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9112 4297 94 92 9112 4297 9155 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9075 4350 5\001
|
|
||||||
-6
|
|
||||||
6 8865 3420 9090 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 8977 3532 94 92 8977 3532 9020 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 8940 3585 7\001
|
|
||||||
-6
|
|
||||||
6 9315 3150 9540 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9427 3262 94 92 9427 3262 9470 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9390 3315 0\001
|
|
||||||
-6
|
|
||||||
6 9405 3690 9630 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9517 3802 94 92 9517 3802 9560 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9480 3855 8\001
|
|
||||||
-6
|
|
||||||
6 9450 4275 9675 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9562 4387 94 92 9562 4387 9605 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9525 4440 4\001
|
|
||||||
-6
|
|
||||||
6 5760 2835 7020 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 7132.500 1777.500 6075 3555 6345 3690 6615 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5917.500 3532.500 6570 3285 6615 3555 6570 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 6763.500 4365.900 6615 3825 6300 4050 6210 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 6367.500 3532.500 6525 3285 6210 3285 6075 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 6367.500 4162.500 6615 3870 6750 4140 6660 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 6460.500 4237.500 6210 4320 6435 4500 6660 4410
|
|
||||||
6 6120 4185 6345 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6232 4297 94 92 6232 4297 6275 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6195 4350 5\001
|
|
||||||
-6
|
|
||||||
6 5985 3420 6210 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6097 3532 94 92 6097 3532 6140 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6060 3585 7\001
|
|
||||||
-6
|
|
||||||
6 6435 3150 6660 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6547 3262 94 92 6547 3262 6590 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6510 3315 0\001
|
|
||||||
-6
|
|
||||||
6 6525 3690 6750 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6637 3802 94 92 6637 3802 6680 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6600 3855 8\001
|
|
||||||
-6
|
|
||||||
6 6570 4275 6795 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6682 4387 94 92 6682 4387 6725 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6645 4440 4\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
6030 2835 6120 3105
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
6113 4891 6293 4666
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 5760 3105 b)\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 5895 4365 g:3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 5760 3555 g:4\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 6480 3105 g:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6120 3240 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6345 3645 4\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6660 3555 1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6795 4185 2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6300 4635 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6210 4005 3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 6795 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 6570 4635 g:2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 5355 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 3105 a)\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8775 4365 g:3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8640 3555 g:6\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 9360 3105 g:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9000 3240 7\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9225 3645 6\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9540 3555 1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9675 4185 2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9180 4635 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9090 4005 3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 9675 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 9450 4635 g:2\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 8640 3105 d)\001
|
|
||||||
|
|
@ -1,180 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 6210.000 5940.000 5985 5400 6210 5355 6435 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 6210.000 5940.000 6435 6480 6210 6525 5985 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7740.000 5940.000 7515 5400 7740 5355 7965 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7740.000 5940.000 7965 6480 7740 6525 7515 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 9270.000 5940.000 9045 5400 9270 5355 9495 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 9270.000 5940.000 9495 6480 9270 6525 9045 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4860.000 5940.000 4635 5400 4860 5355 5085 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4860.000 5940.000 5085 6480 4860 6525 4635 6480
|
|
||||||
6 5895 5310 6075 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5985 5400 90 90 5985 5400 6075 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5955 5437 7\001
|
|
||||||
-6
|
|
||||||
6 6345 5310 6525 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 6435 5400 90 90 6435 5400 6525 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6405 5437 0\001
|
|
||||||
-6
|
|
||||||
6 6345 6390 6525 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 6435 6480 90 90 6435 6480 6525 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6405 6517 3\001
|
|
||||||
-6
|
|
||||||
6 5895 6390 6075 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5985 6480 90 90 5985 6480 6075 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5955 6517 4\001
|
|
||||||
-6
|
|
||||||
6 6120 5850 6300 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 6210 5940 90 90 6210 5940 6300 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6180 5977 8\001
|
|
||||||
-6
|
|
||||||
6 7425 5310 7605 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7515 5400 90 90 7515 5400 7605 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7485 5437 7\001
|
|
||||||
-6
|
|
||||||
6 7875 5310 8055 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7965 5400 90 90 7965 5400 8055 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7935 5437 0\001
|
|
||||||
-6
|
|
||||||
6 7875 6390 8055 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7965 6480 90 90 7965 6480 8055 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7935 6517 3\001
|
|
||||||
-6
|
|
||||||
6 7425 6390 7605 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7515 6480 90 90 7515 6480 7605 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7485 6517 4\001
|
|
||||||
-6
|
|
||||||
6 7650 5850 7830 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7740 5940 90 90 7740 5940 7830 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7710 5977 8\001
|
|
||||||
-6
|
|
||||||
6 8955 5310 9135 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9045 5400 90 90 9045 5400 9135 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9015 5437 7\001
|
|
||||||
-6
|
|
||||||
6 9405 5310 9585 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9495 5400 90 90 9495 5400 9585 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9465 5437 0\001
|
|
||||||
-6
|
|
||||||
6 9405 6390 9585 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9495 6480 90 90 9495 6480 9585 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9465 6517 3\001
|
|
||||||
-6
|
|
||||||
6 8955 6390 9135 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9045 6480 90 90 9045 6480 9135 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9015 6517 4\001
|
|
||||||
-6
|
|
||||||
6 9180 5850 9360 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9270 5940 90 90 9270 5940 9360 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9240 5977 8\001
|
|
||||||
-6
|
|
||||||
6 4545 5310 4725 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4635 5400 90 90 4635 5400 4725 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4605 5437 7\001
|
|
||||||
-6
|
|
||||||
6 4995 5310 5175 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5085 5400 90 90 5085 5400 5175 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5055 5437 0\001
|
|
||||||
-6
|
|
||||||
6 4995 6390 5175 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5085 6480 90 90 5085 6480 5175 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5055 6517 3\001
|
|
||||||
-6
|
|
||||||
6 4545 6390 4725 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4635 6480 90 90 4635 6480 4725 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4605 6517 4\001
|
|
||||||
-6
|
|
||||||
6 4770 5850 4950 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4860 5940 90 90 4860 5940 4950 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4830 5977 8\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 6435 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 5985 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 6435 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 5985 6480
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 0 1 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
6255 5220 6615 5040
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
5760 6840 6120 6660
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7965 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7515 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7965 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7515 6480
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7290 6840 7650 6660
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7110 5895 7470 5715
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9495 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9045 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9495 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9045 6480
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 5085 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 4635 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 5085 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 4635 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 6345 5985 g:0\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 6570 5310 g:1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 5715 5310 g:4\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6165 5310 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5985 5715 4\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5985 6255 3\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6390 6255 2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6390 5715 1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6165 6660 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 6525 6660 g:2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 5715 6660 g:3\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 5490 5445 b)\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 7875 5985 g:0\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8100 5310 g:1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 7245 5310 g:5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7695 5310 6\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7515 5715 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7515 6255 3\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7920 6255 2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7920 5715 1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7695 6660 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8055 6660 g:2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 7245 6660 g:3\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 7020 5445 c)\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 9405 5985 g:0\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 9630 5310 g:1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8775 5310 g:6\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9225 5310 7\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9045 5715 6\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9045 6255 3\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9450 6255 2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9450 5715 1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9225 6660 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 9585 6660 g:2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8775 6660 g:3\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 8550 5445 d)\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 4995 5985 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 5445 a)\001
|
|
||||||
|
|
@ -1,124 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1102.500 1462.500 1755 1215 1800 1440 1755 1710
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 2992.500 1462.500 3645 1215 3690 1440 3645 1710
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5107.500 1462.500 5760 1215 5805 1440 5760 1710
|
|
||||||
6 585 1125 765 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 675 1215 90 90 675 1215 765 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 645 1252 6\001
|
|
||||||
-6
|
|
||||||
6 585 1575 765 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 675 1665 90 90 675 1665 765 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 645 1702 5\001
|
|
||||||
-6
|
|
||||||
6 1125 1350 1305 1530
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1215 1440 90 90 1215 1440 1305 1440
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1185 1477 8\001
|
|
||||||
-6
|
|
||||||
6 1665 1575 1845 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 1755 1665 90 90 1755 1665 1845 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1725 1702 2\001
|
|
||||||
-6
|
|
||||||
6 1665 1125 1845 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 1755 1215 90 90 1755 1215 1845 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1725 1252 1\001
|
|
||||||
-6
|
|
||||||
6 1035 1890 1395 2070
|
|
||||||
6 1035 1890 1215 2070
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1035 1890 1215 1890 1215 2070 1035 2070 1035 1890
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 1095 2017 0\001
|
|
||||||
-6
|
|
||||||
6 1215 1890 1395 2070
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1215 1890 1395 1890 1395 2070 1215 2070 1215 1890
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 1275 2017 4\001
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
6 2475 1125 2655 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2565 1215 90 90 2565 1215 2655 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2535 1252 6\001
|
|
||||||
-6
|
|
||||||
6 2475 1575 2655 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2565 1665 90 90 2565 1665 2655 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2535 1702 5\001
|
|
||||||
-6
|
|
||||||
6 3015 1350 3195 1530
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3105 1440 90 90 3105 1440 3195 1440
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3075 1477 8\001
|
|
||||||
-6
|
|
||||||
6 3555 1575 3735 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3645 1665 90 90 3645 1665 3735 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3615 1702 2\001
|
|
||||||
-6
|
|
||||||
6 3555 1125 3735 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3645 1215 90 90 3645 1215 3735 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3615 1252 1\001
|
|
||||||
-6
|
|
||||||
6 3015 1890 3195 2070
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3015 1890 3195 1890 3195 2070 3015 2070 3015 1890
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 3075 2017 4\001
|
|
||||||
-6
|
|
||||||
6 4590 1125 4770 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 1215 90 90 4680 1215 4770 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 1252 6\001
|
|
||||||
-6
|
|
||||||
6 4590 1575 4770 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 1665 90 90 4680 1665 4770 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 1702 5\001
|
|
||||||
-6
|
|
||||||
6 5130 1350 5310 1530
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5220 1440 90 90 5220 1440 5310 1440
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5190 1477 8\001
|
|
||||||
-6
|
|
||||||
6 5670 1575 5850 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 1665 90 90 5760 1665 5850 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 1702 2\001
|
|
||||||
-6
|
|
||||||
6 5670 1125 5850 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 1215 90 90 5760 1215 5850 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 1252 1\001
|
|
||||||
-6
|
|
||||||
6 5130 1935 5265 2070
|
|
||||||
1 1 0 1 0 33 45 -1 40 0.000 1 0.0000 5217 2000 44 52 5217 2000 5239 2045
|
|
||||||
2 1 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 2
|
|
||||||
5235 1940 5198 2061
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1215 1440 1755 1215
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1216 1443 1756 1218
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3105 1440 3645 1215
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3106 1443 3646 1218
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 1440 5760 1215
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5221 1443 5761 1218
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 945 1485 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 1110 630 2250 UnAssignedAddresses\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2835 1485 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 3285 1305 0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 1110 2520 2250 UnAssignedAddresses\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 4950 1485 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 5400 1305 0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 1110 4635 2250 UnAssignedAddresses\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 4590 1890 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 5670 1890 g:4\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 5670 1080 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 4590 1080 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 1125 c)\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3555 1080 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 2205 1125 b)\001
|
|
||||||
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|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 5850 1485 4\001
|
|
||||||
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|
|
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|
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|
|
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|
|
||||||
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|
|
||||||
6 -2700 3060 -540 3240
|
|
||||||
6 -2700 3060 -540 3240
|
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|
|
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2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
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|
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2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
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|
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|
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|
|
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|
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6 -2700 5085 -540 5265
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6 -2700 5085 -540 5265
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|
||||||
8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine
|
|
||||||
8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf
|
|
||||||
8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute
|
|
||||||
8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring
|
|
||||||
8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute
|
|
||||||
8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute
|
|
||||||
8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve
|
|
||||||
8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply
|
|
||||||
8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex
|
|
||||||
8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave
|
|
||||||
8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring
|
|
||||||
8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute
|
|
||||||
8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute
|
|
||||||
8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve
|
|
||||||
8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide
|
|
||||||
8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex
|
|
||||||
8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def
|
|
||||||
/Times-Roman /Times-Roman-iso isovec ReEncode
|
|
||||||
/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
|
|
||||||
/$F2psEnd {$F2psEnteredState restore end} def
|
|
||||||
|
|
||||||
$F2psBegin
|
|
||||||
10 setmiterlimit
|
|
||||||
0 slj 0 slc
|
|
||||||
0.06299 0.06299 sc
|
|
||||||
%
|
|
||||||
% Fig objects follow
|
|
||||||
%
|
|
||||||
%
|
|
||||||
% here starts figure with depth 45
|
|
||||||
% Polyline
|
|
||||||
0 slj
|
|
||||||
0 slc
|
|
||||||
7.500 slw
|
|
||||||
n -2700 3060 m -2430 3060 l -2430 3240 l -2700 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2430 3060 m -2160 3060 l -2160 3240 l -2430 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2160 3060 m -1890 3060 l -1890 3240 l -2160 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1890 3060 m -1620 3060 l -1620 3240 l -1890 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1620 3060 m -1350 3060 l -1350 3240 l -1620 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1350 3060 m -1080 3060 l -1080 3240 l -1350 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1080 3060 m -810 3060 l -810 3240 l -1080 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -810 3060 m -540 3060 l -540 3240 l -810 3240 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2610 2970 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-765 2970 m
|
|
||||||
gs 1 -1 sc (n-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 285.75 scf sf
|
|
||||||
-1575 2970 m
|
|
||||||
gs 1 -1 sc (...) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2070 2970 m
|
|
||||||
gs 1 -1 sc (2) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2340 2970 m
|
|
||||||
gs 1 -1 sc (1) col0 sh gr
|
|
||||||
% Polyline
|
|
||||||
n -2700 4455 m -2430 4455 l -2430 4635 l -2700 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2430 4455 m -2160 4455 l -2160 4635 l -2430 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2160 4455 m -1890 4455 l -1890 4635 l -2160 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1890 4455 m -1620 4455 l -1620 4635 l -1890 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1620 4455 m -1350 4455 l -1350 4635 l -1620 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1350 4455 m -1080 4455 l -1080 4635 l -1350 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1080 4455 m -810 4455 l -810 4635 l -1080 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -810 4455 m -540 4455 l -540 4635 l -810 4635 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2700 5085 m -2430 5085 l -2430 5265 l -2700 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2430 5085 m -2160 5085 l -2160 5265 l -2430 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2160 5085 m -1890 5085 l -1890 5265 l -2160 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1890 5085 m -1620 5085 l -1620 5265 l -1890 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1620 5085 m -1350 5085 l -1350 5265 l -1620 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1350 5085 m -1080 5085 l -1080 5265 l -1350 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1080 5085 m -810 5085 l -810 5265 l -1080 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -810 5085 m -540 5085 l -540 5265 l -810 5265 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2610 4365 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-765 4365 m
|
|
||||||
gs 1 -1 sc (n-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 285.75 scf sf
|
|
||||||
-1575 4365 m
|
|
||||||
gs 1 -1 sc (...) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2070 4365 m
|
|
||||||
gs 1 -1 sc (2) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2340 4365 m
|
|
||||||
gs 1 -1 sc (1) col0 sh gr
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2073 5050 m -1986 5117 l -1949 5070 l -2037 5002 l -2037 5002 l -1996 5072 l -2073 5050 l cp
|
|
||||||
eoclip
|
|
||||||
n -2565 4635 m
|
|
||||||
-1980 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2073 5050 m -1996 5072 l -2037 5002 l -2043 5035 l -2073 5050 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2540 4987 m -2598 5082 l -2546 5113 l -2488 5018 l -2488 5018 l -2553 5067 l -2540 4987 l cp
|
|
||||||
eoclip
|
|
||||||
n -2295 4635 m
|
|
||||||
-2565 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2540 4987 m -2553 5067 l -2488 5018 l -2522 5015 l -2540 4987 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2263 4989 m -2328 5080 l -2279 5114 l -2214 5023 l -2214 5023 l -2282 5068 l -2263 4989 l cp
|
|
||||||
eoclip
|
|
||||||
n -1980 4635 m
|
|
||||||
-2295 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2263 4989 m -2282 5068 l -2214 5023 l -2247 5018 l -2263 4989 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-997 5066 m -900 5118 l -872 5065 l -969 5013 l -969 5013 l -917 5075 l -997 5066 l cp
|
|
||||||
eoclip
|
|
||||||
n -1755 4635 m
|
|
||||||
-900 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -997 5066 m -917 5075 l -969 5013 l -970 5047 l -997 5066 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1730 4987 m -1788 5082 l -1736 5113 l -1678 5018 l -1678 5018 l -1743 5067 l -1730 4987 l cp
|
|
||||||
eoclip
|
|
||||||
n -1485 4635 m
|
|
||||||
-1755 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1730 4987 m -1743 5067 l -1678 5018 l -1712 5015 l -1730 4987 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1460 4987 m -1518 5082 l -1466 5113 l -1408 5018 l -1408 5018 l -1473 5067 l -1460 4987 l cp
|
|
||||||
eoclip
|
|
||||||
n -1215 4635 m
|
|
||||||
-1485 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1460 4987 m -1473 5067 l -1408 5018 l -1442 5015 l -1460 4987 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1159 5000 m -1245 5071 l -1207 5117 l -1121 5047 l -1121 5047 l -1198 5072 l -1159 5000 l cp
|
|
||||||
eoclip
|
|
||||||
n -675 4635 m
|
|
||||||
-1215 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1159 5000 m -1198 5072 l -1121 5047 l -1151 5033 l -1159 5000 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-749 5018 m -693 5113 l -641 5082 l -697 4987 l -697 4987 l -685 5067 l -749 5018 l cp
|
|
||||||
eoclip
|
|
||||||
n -945 4635 m
|
|
||||||
-675 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -749 5018 m -685 5067 l -697 4987 l -715 5015 l -749 5018 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-450 5220 m
|
|
||||||
gs 1 -1 sc (Hash Table) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-450 4590 m
|
|
||||||
gs 1 -1 sc (Key Set) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2610 5490 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-765 5490 m
|
|
||||||
gs 1 -1 sc (n-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2070 5490 m
|
|
||||||
gs 1 -1 sc (2) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2340 5490 m
|
|
||||||
gs 1 -1 sc (1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 285.75 scf sf
|
|
||||||
-1575 5445 m
|
|
||||||
gs 1 -1 sc (...) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 174.63 scf sf
|
|
||||||
-3600 4860 m
|
|
||||||
gs 1 -1 sc (\(b\)) col0 sh gr
|
|
||||||
% Polyline
|
|
||||||
n -1890 3690 m -1620 3690 l -1620 3870 l -1890 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1350 3690 m -1080 3690 l -1080 3870 l -1350 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1080 3690 m -810 3690 l -810 3870 l -1080 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -810 3690 m -540 3690 l -540 3870 l -810 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -3240 3690 m -2970 3690 l -2970 3870 l -3240 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -270 3690 m 0 3690 l 0 3870 l -270 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2970 3690 m -2700 3690 l -2700 3870 l -2970 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2700 3690 m -2430 3690 l -2430 3870 l -2700 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2430 3690 m -2160 3690 l -2160 3870 l -2430 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1620 3690 m -1350 3690 l -1350 3870 l -1620 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -540 3690 m -270 3690 l -270 3870 l -540 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2160 3690 m -1890 3690 l -1890 3870 l -2160 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2116 3652 m -2032 3722 l -1994 3676 l -2078 3605 l -2078 3605 l -2040 3677 l -2116 3652 l cp
|
|
||||||
eoclip
|
|
||||||
n -2565 3240 m
|
|
||||||
-2025 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2116 3652 m -2040 3677 l -2078 3605 l -2086 3638 l -2116 3652 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2540 3592 m -2598 3687 l -2546 3718 l -2488 3623 l -2488 3623 l -2553 3672 l -2540 3592 l cp
|
|
||||||
eoclip
|
|
||||||
n -2295 3240 m
|
|
||||||
-2565 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2540 3592 m -2553 3672 l -2488 3623 l -2522 3620 l -2540 3592 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-3071 3626 m -3175 3667 l -3152 3723 l -3049 3682 l -3049 3682 l -3130 3682 l -3071 3626 l cp
|
|
||||||
eoclip
|
|
||||||
n -2025 3240 m
|
|
||||||
-3150 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -3071 3626 m -3130 3682 l -3049 3682 l -3074 3659 l -3071 3626 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1306 3652 m -1222 3722 l -1184 3676 l -1268 3605 l -1268 3605 l -1230 3677 l -1306 3652 l cp
|
|
||||||
eoclip
|
|
||||||
n -1755 3240 m
|
|
||||||
-1215 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1306 3652 m -1230 3677 l -1268 3605 l -1276 3638 l -1306 3652 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1730 3592 m -1788 3687 l -1736 3718 l -1678 3623 l -1678 3623 l -1743 3672 l -1730 3592 l cp
|
|
||||||
eoclip
|
|
||||||
n -1485 3240 m
|
|
||||||
-1755 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1730 3592 m -1743 3672 l -1678 3623 l -1712 3620 l -1730 3592 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-188 3682 m -87 3723 l -64 3667 l -166 3626 l -166 3626 l -108 3682 l -188 3682 l cp
|
|
||||||
eoclip
|
|
||||||
n -1215 3240 m
|
|
||||||
-90 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -188 3682 m -108 3682 l -166 3626 l -163 3659 l -188 3682 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-920 3592 m -978 3687 l -926 3718 l -868 3623 l -868 3623 l -933 3672 l -920 3592 l cp
|
|
||||||
eoclip
|
|
||||||
n -675 3240 m
|
|
||||||
-945 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -920 3592 m -933 3672 l -868 3623 l -902 3620 l -920 3592 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-749 3623 m -693 3718 l -641 3687 l -697 3592 l -697 3592 l -685 3672 l -749 3623 l cp
|
|
||||||
eoclip
|
|
||||||
n -945 3240 m
|
|
||||||
-675 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -749 3623 m -685 3672 l -697 3592 l -715 3620 l -749 3623 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2610 4095 m
|
|
||||||
gs 1 -1 sc (2) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2880 4095 m
|
|
||||||
gs 1 -1 sc (1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-3150 4095 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 285.75 scf sf
|
|
||||||
-1575 4050 m
|
|
||||||
gs 1 -1 sc (...) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-270 4095 m
|
|
||||||
gs 1 -1 sc (m-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-450 3195 m
|
|
||||||
gs 1 -1 sc (Key Set) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
90 3825 m
|
|
||||||
gs 1 -1 sc (Hash Table) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 174.63 scf sf
|
|
||||||
-3600 3465 m
|
|
||||||
gs 1 -1 sc (\(a\)) col0 sh gr
|
|
||||||
% here ends figure;
|
|
||||||
$F2psEnd
|
|
||||||
rs
|
|
||||||
showpage
|
|
||||||
%%Trailer
|
|
||||||
%EOF
|
|
||||||
|
|
@ -1,86 +0,0 @@
|
||||||
\section{Introduction}
|
|
||||||
\label{sec:introduction}
|
|
||||||
|
|
||||||
Suppose~$U$ is a universe of \textit{keys}.
|
|
||||||
Let $h:U\to M$ be a {\em hash function} that maps the keys from~$U$
|
|
||||||
to a given interval of integers $M=[0,m-1]=\{0,1,\dots,m-1\}$.
|
|
||||||
Let~$S\subseteq U$ be a set of~$n$ keys from~$U$.
|
|
||||||
Given a key~$x\in S$, the hash function~$h$ computes an integer in
|
|
||||||
$[0,m-1]$ for the storage or retrieval of~$x$ in a {\em hash table}.
|
|
||||||
Hashing methods for {\em non-static sets} of keys can be used to construct
|
|
||||||
data structures storing $S$ and supporting membership queries
|
|
||||||
``$x \in S$?'' in expected time $O(1)$.
|
|
||||||
However, they involve a certain amount of wasted space owing to unused
|
|
||||||
locations in the table and waisted time to resolve collisions when
|
|
||||||
two keys are hashed to the same table location.
|
|
||||||
|
|
||||||
For {\em static sets} of keys it is possible to compute a function
|
|
||||||
to find any key in a table in one probe; such hash functions are called
|
|
||||||
\textit{perfect}.
|
|
||||||
Given a set of keys~$S$, we shall say that a hash function~$h:U\to M$ is a
|
|
||||||
\textit{perfect hash function} for~$S$ if~$h$ is an injection on~$S$,
|
|
||||||
that is, there are no \textit{collisions} among the keys in~$S$: if~$x$
|
|
||||||
and~$y$ are in~$S$ and~$x\neq y$, then~$h(x)\neq h(y)$.
|
|
||||||
Figure~\ref{fig:minimalperfecthash-ph-mph}(a) illustrates a perfect hash
|
|
||||||
function.
|
|
||||||
Since no collisions occur, each key can be retrieved from the table
|
|
||||||
with a single probe.
|
|
||||||
If~$m=n$, that is, the table has the same size as~$S$,
|
|
||||||
then~$h$ is a \textit{minimal perfect hash function} for~$S$.
|
|
||||||
Figure~\ref{fig:minimalperfecthash-ph-mph}(b) illustrates
|
|
||||||
a~minimal perfect hash function.
|
|
||||||
Minimal perfect hash functions totally avoid the problem of wasted
|
|
||||||
space and time.
|
|
||||||
|
|
||||||
% For two-column wide figures use
|
|
||||||
\begin{figure*}
|
|
||||||
% Use the relevant command to insert your figure file.
|
|
||||||
% For example, with the graphicx package use
|
|
||||||
\centering
|
|
||||||
\includegraphics{figs/minimalperfecthash-ph-mph.ps}
|
|
||||||
% figure caption is below the figure
|
|
||||||
\caption{(a) Perfect hash function\quad (b) Minimal perfect hash function}
|
|
||||||
\label{fig:minimalperfecthash-ph-mph}
|
|
||||||
\end{figure*}
|
|
||||||
|
|
||||||
Minimal perfect hash functions are widely used for memory efficient
|
|
||||||
storage
|
|
||||||
and fast retrieval of items from static sets, such as words in natural
|
|
||||||
languages, reserved words in programming languages or interactive systems,
|
|
||||||
universal resource locations (URLs) in Web search engines, or item sets in
|
|
||||||
data mining techniques.
|
|
||||||
|
|
||||||
The aim of this paper is to describe a new way of constructing minimal perfect
|
|
||||||
hash functions. Our algorithm shares several features with the one due to
|
|
||||||
Czech, Havas and Majewski~\cite{chm92}. In particular, our algorithm is also
|
|
||||||
based on the generation of random graphs~$G=(V,E)$, where~$E$ is in one-to-one
|
|
||||||
correspondence with the key set~$S$ for which we wish to generate the hash
|
|
||||||
function.
|
|
||||||
The two main differences between our algorithm and theirs
|
|
||||||
are as follows:
|
|
||||||
(\textit{i})~we generate random graphs
|
|
||||||
$G = (V, E)$ with $|V|=cn$ and $|E|=|S|=n$, where~$c=1.15$, and hence~$G$
|
|
||||||
contains cycles with high probability,
|
|
||||||
while they generate \textit{acyclic} random graphs
|
|
||||||
$G = (V, E)$ with $|V|=cn$ and $|E|=|S|=n$,
|
|
||||||
with a greater number of vertices: $|V|\ge2.09n$;
|
|
||||||
(\textit{ii})~they generate order preserving minimal perfect hash functions
|
|
||||||
while our algorithm does not preserve order (a perfect hash function $h$ is
|
|
||||||
\textit{order preserving} if the keys in~$S$ are arranged in some given order
|
|
||||||
and~$h$ preserves this order in the hash table). Thus, our algorithm improves
|
|
||||||
the space requirement at the expense of generating functions that are not
|
|
||||||
order preserving.
|
|
||||||
|
|
||||||
Our algorithm is efficient and may be tuned to yield a function~$h$
|
|
||||||
with a very economical description.
|
|
||||||
As the algorithm in~\cite{chm92}, our algorithm produces~$h$
|
|
||||||
in~$O(n)$ expected time for a set of~$n$ keys.
|
|
||||||
The description of~$h$ requires~$1.15n$ computer words,
|
|
||||||
and evaluating~$h(x)$
|
|
||||||
requires two accesses to an array of~$1.15n$ integers.
|
|
||||||
We further derive a heuristic that improves the space requirement
|
|
||||||
from~$1.15n$ words down to~$0.93n$ words.
|
|
||||||
Our scheme is very practical: to generate a minimal perfect hash function for
|
|
||||||
a collection of 100~million universe resource locations (URLs), each 63 bytes
|
|
||||||
long on average, our algorithm running on a commodity PC takes 811 seconds on
|
|
||||||
average.
|
|
||||||
|
|
@ -1,17 +0,0 @@
|
||||||
all:
|
|
||||||
latex vldb.tex
|
|
||||||
bibtex vldb
|
|
||||||
latex vldb.tex
|
|
||||||
latex vldb.tex
|
|
||||||
dvips vldb.dvi -o vldb.ps
|
|
||||||
ps2pdf vldb.ps
|
|
||||||
chmod -R g+rwx *
|
|
||||||
|
|
||||||
perm:
|
|
||||||
chmod -R g+rwx *
|
|
||||||
|
|
||||||
run: clean all
|
|
||||||
gv vldb.ps &
|
|
||||||
clean:
|
|
||||||
rm *.aux *.bbl *.blg *.log
|
|
||||||
|
|
||||||
|
|
@ -1,687 +0,0 @@
|
||||||
@inproceedings{p99,
|
|
||||||
author = {R. Pagh},
|
|
||||||
title = {Hash and Displace: Efficient Evaluation of Minimal Perfect Hash Functions},
|
|
||||||
booktitle = {Workshop on Algorithms and Data Structures},
|
|
||||||
pages = {49-54},
|
|
||||||
year = 1999,
|
|
||||||
url = {citeseer.nj.nec.com/pagh99hash.html},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{p00,
|
|
||||||
author = {R. Pagh},
|
|
||||||
title = {Faster deterministic dictionaries},
|
|
||||||
journal = {Symposium on Discrete Algorithms (ACM SODA)},
|
|
||||||
OPTvolume = {43},
|
|
||||||
OPTnumber = {5},
|
|
||||||
pages = {487--493},
|
|
||||||
year = {2000}
|
|
||||||
}
|
|
||||||
|
|
||||||
@InProceedings{ss89,
|
|
||||||
author = {P. Schmidt and A. Siegel},
|
|
||||||
title = {On aspects of universality and performance for closed hashing},
|
|
||||||
booktitle = {Proc. 21th Ann. ACM Symp. on Theory of Computing -- STOC'89},
|
|
||||||
month = {May},
|
|
||||||
year = {1989},
|
|
||||||
pages = {355--366}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{asw00,
|
|
||||||
author = {M. Atici and D. R. Stinson and R. Wei.},
|
|
||||||
title = {A new practical algorithm for the construction of a perfect hash function},
|
|
||||||
journal = {Journal Combin. Math. Combin. Comput.},
|
|
||||||
volume = {35},
|
|
||||||
pages = {127--145},
|
|
||||||
year = {2000}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{swz00,
|
|
||||||
author = {D. R. Stinson and R. Wei and L. Zhu},
|
|
||||||
title = {New constructions for perfect hash families and related structures using combinatorial designs and codes},
|
|
||||||
journal = {Journal Combin. Designs.},
|
|
||||||
volume = {8},
|
|
||||||
pages = {189--200},
|
|
||||||
year = {2000}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{ht01,
|
|
||||||
author = {T. Hagerup and T. Tholey},
|
|
||||||
title = {Efficient minimal perfect hashing in nearly minimal space},
|
|
||||||
booktitle = {The 18th Symposium on Theoretical Aspects of Computer Science (STACS), volume 2010 of Lecture Notes in Computer Science},
|
|
||||||
year = 2001,
|
|
||||||
pages = {317--326},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{dh01,
|
|
||||||
author = {M. Dietzfelbinger and T. Hagerup},
|
|
||||||
title = {Simple minimal perfect hashing in less space},
|
|
||||||
booktitle = {The 9th European Symposium on Algorithms (ESA), volume 2161 of Lecture Notes in Computer Science},
|
|
||||||
year = 2001,
|
|
||||||
pages = {109--120},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@MastersThesis{mar00,
|
|
||||||
author = {M. S. Neubert},
|
|
||||||
title = {Algoritmos Distribu<62>os para a Constru<72>o de Arquivos invertidos},
|
|
||||||
school = {Departamento de Ci<43>cia da Computa<74>o, Universidade Federal de Minas Gerais},
|
|
||||||
year = 2000,
|
|
||||||
month = {Mar<61>},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{clrs01,
|
|
||||||
author = {T. H. Cormen and C. E. Leiserson and R. L. Rivest and C. Stein},
|
|
||||||
title = {Introduction to Algorithms},
|
|
||||||
publisher = {MIT Press},
|
|
||||||
year = {2001},
|
|
||||||
edition = {second},
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{k73,
|
|
||||||
author = {D. E. Knuth},
|
|
||||||
title = {The Art of Computer Programming: Sorting and Searching},
|
|
||||||
publisher = {Addison-Wesley},
|
|
||||||
volume = {3},
|
|
||||||
year = {1973},
|
|
||||||
edition = {second},
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{rp99,
|
|
||||||
author = {R. Pagh},
|
|
||||||
title = {Hash and Displace: Efficient Evaluation of Minimal Perfect Hash Functions},
|
|
||||||
booktitle = {Workshop on Algorithms and Data Structures},
|
|
||||||
pages = {49-54},
|
|
||||||
year = 1999,
|
|
||||||
url = {citeseer.nj.nec.com/pagh99hash.html},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{hmwc93,
|
|
||||||
author = {G. Havas and B.S. Majewski and N.C. Wormald and Z.J. Czech},
|
|
||||||
title = {Graphs, Hypergraphs and Hashing},
|
|
||||||
booktitle = {19th International Workshop on Graph-Theoretic Concepts in Computer Science},
|
|
||||||
publisher = {Springer Lecture Notes in Computer Science vol. 790},
|
|
||||||
pages = {153-165},
|
|
||||||
year = 1993,
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{bkz05,
|
|
||||||
author = {F.C. Botelho and Y. Kohayakawa and N. Ziviani},
|
|
||||||
title = {A Practical Minimal Perfect Hashing Method},
|
|
||||||
booktitle = {4th International Workshop on Efficient and Experimental Algorithms},
|
|
||||||
publisher = {Springer Lecture Notes in Computer Science vol. 3503},
|
|
||||||
pages = {488-500},
|
|
||||||
Moth = May,
|
|
||||||
year = 2005,
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{chm97,
|
|
||||||
author = {Z.J. Czech and G. Havas and B.S. Majewski},
|
|
||||||
title = {Fundamental Study Perfect Hashing},
|
|
||||||
journal = {Theoretical Computer Science},
|
|
||||||
volume = {182},
|
|
||||||
year = {1997},
|
|
||||||
pages = {1-143},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{chm92,
|
|
||||||
author = {Z.J. Czech and G. Havas and B.S. Majewski},
|
|
||||||
title = {An Optimal Algorithm for Generating Minimal Perfect Hash Functions},
|
|
||||||
journal = {Information Processing Letters},
|
|
||||||
volume = {43},
|
|
||||||
number = {5},
|
|
||||||
pages = {257-264},
|
|
||||||
year = {1992},
|
|
||||||
url = {citeseer.nj.nec.com/czech92optimal.html},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{mwhc96,
|
|
||||||
author = {B.S. Majewski and N.C. Wormald and G. Havas and Z.J. Czech},
|
|
||||||
title = {A family of perfect hashing methods},
|
|
||||||
journal = {The Computer Journal},
|
|
||||||
year = {1996},
|
|
||||||
volume = {39},
|
|
||||||
number = {6},
|
|
||||||
pages = {547-554},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@InProceedings{bv04,
|
|
||||||
author = {P. Boldi and S. Vigna},
|
|
||||||
title = {The WebGraph Framework I: Compression Techniques},
|
|
||||||
booktitle = {13th International World Wide Web Conference},
|
|
||||||
pages = {595--602},
|
|
||||||
year = {2004}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{z04,
|
|
||||||
author = {N. Ziviani},
|
|
||||||
title = {Projeto de Algoritmos com implementa<74>es em Pascal e C},
|
|
||||||
publisher = {Pioneira Thompson},
|
|
||||||
year = 2004,
|
|
||||||
edition = {segunda edi<64>o}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{p85,
|
|
||||||
author = {E. M. Palmer},
|
|
||||||
title = {Graphical Evolution: An Introduction to the Theory of Random Graphs},
|
|
||||||
publisher = {John Wiley \& Sons},
|
|
||||||
year = {1985},
|
|
||||||
address = {New York}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Book{imb99,
|
|
||||||
author = {I.H. Witten and A. Moffat and T.C. Bell},
|
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|
|
||||||
note = {To Appear},
|
|
||||||
OPTannote = {}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{pw04,
|
|
||||||
author = {B. Pittel and N. C. Wormald},
|
|
||||||
title = {Counting connected graphs inside-out},
|
|
||||||
journal = {Journal of Combinatorial Theory},
|
|
||||||
OPTkey = {},
|
|
||||||
OPTvolume = {},
|
|
||||||
OPTnumber = {},
|
|
||||||
OPTpages = {},
|
|
||||||
OPTmonth = {},
|
|
||||||
note = {To Appear},
|
|
||||||
OPTannote = {}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Article{mr95,
|
|
||||||
author = {M. Molloy and B. Reed},
|
|
||||||
title = {A critical point for random graphs with a given degree sequence},
|
|
||||||
journal = {Random Structures and Algorithms},
|
|
||||||
year = {1995},
|
|
||||||
volume = {6},
|
|
||||||
pages = {161-179}
|
|
||||||
}
|
|
||||||
|
|
||||||
@TechReport{bmz04,
|
|
||||||
author = {F. C. Botelho and D. Menoti and N. Ziviani},
|
|
||||||
title = {A New algorithm for constructing minimal perfect hash functions},
|
|
||||||
institution = {Federal Univ. of Minas Gerais},
|
|
||||||
year = {2004},
|
|
||||||
OPTkey = {},
|
|
||||||
OPTtype = {},
|
|
||||||
number = {TR004},
|
|
||||||
OPTaddress = {},
|
|
||||||
OPTmonth = {},
|
|
||||||
note = {(http://www.dcc.ufmg.br/\texttt{\~ }nivio/pub/technicalreports.html)},
|
|
||||||
OPTannote = {}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{mr98,
|
|
||||||
author = {M. Molloy and B. Reed},
|
|
||||||
title = {The size of the giant component of a random graph with a given degree sequence},
|
|
||||||
journal = {Combinatorics, Probability and Computing},
|
|
||||||
year = {1998},
|
|
||||||
volume = {7},
|
|
||||||
pages = {295-305}
|
|
||||||
}
|
|
||||||
|
|
||||||
@misc{h98,
|
|
||||||
author = {D. Hawking},
|
|
||||||
title = {Overview of TREC-7 Very Large Collection Track (Draft for Notebook)},
|
|
||||||
url = {citeseer.ist.psu.edu/4991.html},
|
|
||||||
year = {1998}}
|
|
||||||
|
|
||||||
@book {jlr00,
|
|
||||||
AUTHOR = {Janson, S. and {\L}uczak, T. and Ruci{\'n}ski, A.},
|
|
||||||
TITLE = {Random graphs},
|
|
||||||
PUBLISHER = {Wiley-Inter.},
|
|
||||||
YEAR = 2000,
|
|
||||||
PAGES = {xii+333},
|
|
||||||
ISBN = {0-471-17541-2},
|
|
||||||
MRCLASS = {05C80 (60C05 82B41)},
|
|
||||||
MRNUMBER = {2001k:05180},
|
|
||||||
MRREVIEWER = {Mark R. Jerrum},
|
|
||||||
}
|
|
||||||
|
|
||||||
@incollection {jlr90,
|
|
||||||
AUTHOR = {Janson, Svante and {\L}uczak, Tomasz and Ruci{\'n}ski,
|
|
||||||
Andrzej},
|
|
||||||
TITLE = {An exponential bound for the probability of nonexistence of a
|
|
||||||
specified subgraph in a random graph},
|
|
||||||
BOOKTITLE = {Random graphs '87 (Pozna\'n, 1987)},
|
|
||||||
PAGES = {73--87},
|
|
||||||
PUBLISHER = {Wiley},
|
|
||||||
ADDRESS = {Chichester},
|
|
||||||
YEAR = 1990,
|
|
||||||
MRCLASS = {05C80 (60C05)},
|
|
||||||
MRNUMBER = {91m:05168},
|
|
||||||
MRREVIEWER = {J. Spencer},
|
|
||||||
}
|
|
||||||
|
|
||||||
@book {b01,
|
|
||||||
AUTHOR = {Bollob{\'a}s, B.},
|
|
||||||
TITLE = {Random graphs},
|
|
||||||
SERIES = {Cambridge Studies in Advanced Mathematics},
|
|
||||||
VOLUME = 73,
|
|
||||||
EDITION = {Second},
|
|
||||||
PUBLISHER = {Cambridge University Press},
|
|
||||||
ADDRESS = {Cambridge},
|
|
||||||
YEAR = 2001,
|
|
||||||
PAGES = {xviii+498},
|
|
||||||
ISBN = {0-521-80920-7; 0-521-79722-5},
|
|
||||||
MRCLASS = {05C80 (60C05)},
|
|
||||||
MRNUMBER = {MR1864966 (2002j:05132)},
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
@ -1,67 +0,0 @@
|
||||||
\section{Related Work}
|
|
||||||
Czech, Havas and Majewski~\cite{chm97} provide a
|
|
||||||
comprehensive survey of the most important theoretical results
|
|
||||||
on perfect hashing.
|
|
||||||
In the following, we review some of those results.
|
|
||||||
|
|
||||||
Fredman, Koml\'os and Szemer\'edi~\cite{FKS84} showed that it is possible to
|
|
||||||
construct space efficient perfect hash functions that can be evaluated in
|
|
||||||
constant time with table sizes that are linear in the number of keys:
|
|
||||||
$m=O(n)$. In their model of computation, an element of the universe~$U$ fits
|
|
||||||
into one machine word, and arithmetic operations and memory accesses have unit
|
|
||||||
cost. Randomized algorithms in the FKS model can construct a perfect hash
|
|
||||||
function in expected time~$O(n)$:
|
|
||||||
this is the case of our algorithm and the works in~\cite{chm92,p99}.
|
|
||||||
|
|
||||||
Many methods for generating minimal perfect hash functions use a
|
|
||||||
{\em mapping}, {\em ordering} and {\em searching}
|
|
||||||
(MOS) approach,
|
|
||||||
a description coined by Fox, Chen and Heath~\cite{fch92}.
|
|
||||||
In the MOS approach, the construction of a minimal perfect hash function
|
|
||||||
is accomplished in three steps.
|
|
||||||
First, the mapping step transforms the key set from the original universe
|
|
||||||
to a new universe.
|
|
||||||
Second, the ordering step places the keys in a sequential order that
|
|
||||||
determines the order in which hash values are assigned to keys.
|
|
||||||
Third, the searching step attempts to assign hash values to the keys.
|
|
||||||
Our algorithm and the algorithm presented in~\cite{chm92} use the
|
|
||||||
MOS approach.
|
|
||||||
|
|
||||||
Pagh~\cite{p99} proposed a family of randomized algorithms for
|
|
||||||
constructing minimal perfect hash functions.
|
|
||||||
The form of the resulting function is $h(x) = (f(x) + d_{g(x)}) \bmod n$,
|
|
||||||
where $f$ and $g$ are universal hash functions and $d$ is a set of
|
|
||||||
displacement values to resolve collisions that are caused by the function $f$.
|
|
||||||
Pagh identified a set of conditions concerning $f$ and $g$ and showed
|
|
||||||
that if these conditions are satisfied, then a minimal perfect hash
|
|
||||||
function can be computed in expected time $O(n)$ and stored in
|
|
||||||
$(2+\epsilon)n$ computer words.
|
|
||||||
Dietzfelbinger and Hagerup~\cite{dh01} improved~\cite{p99},
|
|
||||||
reducing from $(2+\epsilon)n$ to $(1+\epsilon)n$ the number of computer
|
|
||||||
words required to store the function, but in their approach~$f$ and~$g$ must
|
|
||||||
be chosen from a class
|
|
||||||
of hash functions that meet additional requirements.
|
|
||||||
Differently from the works in~\cite{p99,dh01}, our algorithm uses two
|
|
||||||
universal hash functions $h_1$ and $h_2$ randomly selected from a class
|
|
||||||
of universal hash functions that do not need to meet any additional
|
|
||||||
requirements.
|
|
||||||
|
|
||||||
The work in~\cite{chm92} presents an efficient and practical algorithm
|
|
||||||
for generating order preserving minimal perfect hash functions.
|
|
||||||
Their method involves the generation of acyclic random graphs
|
|
||||||
$G = (V, E)$ with~$|V|=cn$ and $|E|=n$, with $c \ge 2.09$.
|
|
||||||
They showed that an order preserving minimal perfect hash function
|
|
||||||
can be found in optimal time if~$G$ is acyclic.
|
|
||||||
To generate an acyclic graph, two vertices $h_1(x)$ and $h_2(x)$ are
|
|
||||||
computed for each key $x \in S$.
|
|
||||||
Thus, each set~$S$ has a corresponding graph~$G=(V,E)$, where $V=\{0,1,
|
|
||||||
\ldots,t\}$ and $E=\big\{\{h_1(x),h_2(x)\}:x \in S\big\}$.
|
|
||||||
In order to guarantee the acyclicity of~$G$, the algorithm repeatedly selects
|
|
||||||
$h_1$ and $h_2$ from a family of universal hash functions
|
|
||||||
until the corresponding graph is acyclic.
|
|
||||||
Havas et al.~\cite{hmwc93} proved that if $|V(G)|=cn$ and $c>2$,
|
|
||||||
then the probability that~$G$ is acyclic is $p=e^{1/c}\sqrt{(c-2)/c}$.
|
|
||||||
For $c=2.09$, this probability is
|
|
||||||
$p \simeq 0.342$, and
|
|
||||||
the expected number of iterations to obtain an acyclic graph
|
|
||||||
is~$1/p \simeq 2.92$.
|
|
||||||
|
|
@ -1,77 +0,0 @@
|
||||||
% SVJour2 DOCUMENT CLASS OPTION SVGLOV2 -- for standardised journals
|
|
||||||
%
|
|
||||||
% This is an enhancement for the LaTeX
|
|
||||||
% SVJour2 document class for Springer journals
|
|
||||||
%
|
|
||||||
%%
|
|
||||||
%%
|
|
||||||
%% \CharacterTable
|
|
||||||
%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
|
|
||||||
%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
|
|
||||||
%% Digits \0\1\2\3\4\5\6\7\8\9
|
|
||||||
%% Exclamation \! Double quote \" Hash (number) \#
|
|
||||||
%% Dollar \$ Percent \% Ampersand \&
|
|
||||||
%% Acute accent \' Left paren \( Right paren \)
|
|
||||||
%% Asterisk \* Plus \+ Comma \,
|
|
||||||
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|
|
||||||
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|
|
||||||
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|
|
||||||
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|
|
||||||
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|
|
||||||
%% Grave accent \` Left brace \{ Vertical bar \|
|
|
||||||
%% Right brace \} Tilde \~}
|
|
||||||
\ProvidesFile{svglov2.clo}
|
|
||||||
[2004/10/25 v2.1
|
|
||||||
style option for standardised journals]
|
|
||||||
\typeout{SVJour Class option: svglov2.clo for standardised journals}
|
|
||||||
\def\validfor{svjour2}
|
|
||||||
\ExecuteOptions{final,10pt,runningheads}
|
|
||||||
% No size changing allowed, hence a copy of size10.clo is included
|
|
||||||
\renewcommand\normalsize{%
|
|
||||||
\@setfontsize\normalsize{10.2pt}{4mm}%
|
|
||||||
\abovedisplayskip=3 mm plus6pt minus 4pt
|
|
||||||
\belowdisplayskip=3 mm plus6pt minus 4pt
|
|
||||||
\abovedisplayshortskip=0.0 mm plus6pt
|
|
||||||
\belowdisplayshortskip=2 mm plus4pt minus 4pt
|
|
||||||
\let\@listi\@listI}
|
|
||||||
\normalsize
|
|
||||||
\newcommand\small{%
|
|
||||||
\@setfontsize\small{8.7pt}{3.25mm}%
|
|
||||||
\abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@
|
|
||||||
\abovedisplayshortskip \z@ \@plus2\p@
|
|
||||||
\belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@
|
|
||||||
\def\@listi{\leftmargin\leftmargini
|
|
||||||
\parsep 0\p@ \@plus1\p@ \@minus\p@
|
|
||||||
\topsep 4\p@ \@plus2\p@ \@minus4\p@
|
|
||||||
\itemsep0\p@}%
|
|
||||||
\belowdisplayskip \abovedisplayskip
|
|
||||||
}
|
|
||||||
\let\footnotesize\small
|
|
||||||
\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}
|
|
||||||
\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}
|
|
||||||
\newcommand\large{\@setfontsize\large\@xiipt{14pt}}
|
|
||||||
\newcommand\Large{\@setfontsize\Large\@xivpt{16dd}}
|
|
||||||
\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{17dd}}
|
|
||||||
\newcommand\huge{\@setfontsize\huge\@xxpt{25}}
|
|
||||||
\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
|
|
||||||
%
|
|
||||||
%ALT% \def\runheadhook{\rlap{\smash{\lower5pt\hbox to\textwidth{\hrulefill}}}}
|
|
||||||
\def\runheadhook{\rlap{\smash{\lower11pt\hbox to\textwidth{\hrulefill}}}}
|
|
||||||
\AtEndOfClass{\advance\headsep by5pt}
|
|
||||||
\if@twocolumn
|
|
||||||
\setlength{\textwidth}{17.6cm}
|
|
||||||
\setlength{\textheight}{230mm}
|
|
||||||
\AtEndOfClass{\setlength\columnsep{4mm}}
|
|
||||||
\else
|
|
||||||
\setlength{\textwidth}{11.7cm}
|
|
||||||
\setlength{\textheight}{517.5dd} % 19.46cm
|
|
||||||
\fi
|
|
||||||
%
|
|
||||||
\AtBeginDocument{%
|
|
||||||
\@ifundefined{@journalname}
|
|
||||||
{\typeout{Unknown journal: specify \string\journalname\string{%
|
|
||||||
<name of your journal>\string} in preambel^^J}}{}}
|
|
||||||
%
|
|
||||||
\endinput
|
|
||||||
%%
|
|
||||||
%% End of file `svglov2.clo'.
|
|
||||||
File diff suppressed because it is too large
Load Diff
|
|
@ -1,150 +0,0 @@
|
||||||
%%%%%%%%%%%%%%%%%%%%%%% file template.tex %%%%%%%%%%%%%%%%%%%%%%%%%
|
|
||||||
%
|
|
||||||
% This is a template file for the LaTeX package SVJour2 for the
|
|
||||||
% Springer journal "The VLDB Journal".
|
|
||||||
%
|
|
||||||
% Springer Heidelberg 2004/12/03
|
|
||||||
%
|
|
||||||
% Copy it to a new file with a new name and use it as the basis
|
|
||||||
% for your article. Delete % as needed.
|
|
||||||
%
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
||||||
%
|
|
||||||
% First comes an example EPS file -- just ignore it and
|
|
||||||
% proceed on the \documentclass line
|
|
||||||
% your LaTeX will extract the file if required
|
|
||||||
%\begin{filecontents*}{figs/minimalperfecthash-ph-mph.ps}
|
|
||||||
%!PS-Adobe-3.0 EPSF-3.0
|
|
||||||
%%BoundingBox: 19 19 221 221
|
|
||||||
%%CreationDate: Mon Sep 29 1997
|
|
||||||
%%Creator: programmed by hand (JK)
|
|
||||||
%%EndComments
|
|
||||||
%gsave
|
|
||||||
%newpath
|
|
||||||
% 20 20 moveto
|
|
||||||
% 20 220 lineto
|
|
||||||
% 220 220 lineto
|
|
||||||
% 220 20 lineto
|
|
||||||
%closepath
|
|
||||||
%2 setlinewidth
|
|
||||||
%gsave
|
|
||||||
% .4 setgray fill
|
|
||||||
%grestore
|
|
||||||
%stroke
|
|
||||||
%grestore
|
|
||||||
%\end{filecontents*}
|
|
||||||
%
|
|
||||||
\documentclass[twocolumn,fleqn,runningheads]{svjour2}
|
|
||||||
%
|
|
||||||
\smartqed % flush right qed marks, e.g. at end of proof
|
|
||||||
%
|
|
||||||
\usepackage{graphicx}
|
|
||||||
\usepackage{listings}
|
|
||||||
%
|
|
||||||
% \usepackage{mathptmx} % use Times fonts if available on your TeX system
|
|
||||||
%
|
|
||||||
% insert here the call for the packages your document requires
|
|
||||||
%\usepackage{latexsym}
|
|
||||||
% etc.
|
|
||||||
%
|
|
||||||
% please place your own definitions here and don't use \def but
|
|
||||||
% \newcommand{}{}
|
|
||||||
%
|
|
||||||
|
|
||||||
\lstset{
|
|
||||||
language=Pascal,
|
|
||||||
basicstyle=\fontsize{9}{9}\selectfont,
|
|
||||||
captionpos=t,
|
|
||||||
aboveskip=1mm,
|
|
||||||
belowskip=1mm,
|
|
||||||
abovecaptionskip=1mm,
|
|
||||||
belowcaptionskip=1mm,
|
|
||||||
% numbers = left,
|
|
||||||
mathescape=true,
|
|
||||||
escapechar=@,
|
|
||||||
extendedchars=true,
|
|
||||||
showstringspaces=false,
|
|
||||||
columns=fixed,
|
|
||||||
basewidth=0.515em,
|
|
||||||
frame=single,
|
|
||||||
framesep=2mm,
|
|
||||||
xleftmargin=2mm,
|
|
||||||
xrightmargin=2mm,
|
|
||||||
framerule=0.5pt
|
|
||||||
}
|
|
||||||
|
|
||||||
\def\cG{{\mathcal G}}
|
|
||||||
\def\crit{{\rm crit}}
|
|
||||||
\def\ncrit{{\rm ncrit}}
|
|
||||||
\def\scrit{{\rm scrit}}
|
|
||||||
\def\bedges{{\rm bedges}}
|
|
||||||
\def\ZZ{{\mathbb Z}}
|
|
||||||
|
|
||||||
\journalname{The VLDB Journal}
|
|
||||||
%
|
|
||||||
\begin{document}
|
|
||||||
|
|
||||||
\title{Minimal Perfect Hash Functions: New Algorithms and Applications\thanks{
|
|
||||||
This work was supported in part by
|
|
||||||
GERINDO Project--grant MCT/CNPq/CT-INFO 552.087/02-5,
|
|
||||||
CAPES/PROF Scholarship (Fabiano C. Botelho),
|
|
||||||
FAPESP Proj.\ Tem.\ 03/09925-5 and CNPq Grant 30.0334/93-1
|
|
||||||
(Yoshiharu Kohayakawa),
|
|
||||||
and CNPq Grant 30.5237/02-0 (Nivio Ziviani).}
|
|
||||||
}
|
|
||||||
%\subtitle{Do you have a subtitle?\\ If so, write it here}
|
|
||||||
|
|
||||||
%\titlerunning{Short form of title} % if too long for running head
|
|
||||||
|
|
||||||
\author{Fabiano C. Botelho \and Davi C. Reis \and Yoshiharu Kohayakawa \and Nivio Ziviani}
|
|
||||||
%\authorrunning{Short form of author list} % if too long for running head
|
|
||||||
\institute{
|
|
||||||
F. C. Botelho \and
|
|
||||||
N. Ziviani \at
|
|
||||||
Dept. of Computer Science,
|
|
||||||
Federal Univ. of Minas Gerais,
|
|
||||||
Belo Horizonte, Brazil\\
|
|
||||||
\email{\{fbotelho,nivio\}@dcc.ufmg.br}
|
|
||||||
\and
|
|
||||||
D. C. Reis \at
|
|
||||||
Google, Brazil \\
|
|
||||||
\email{davi.reis@gmail.com}
|
|
||||||
\and
|
|
||||||
Y. Kohayakawa
|
|
||||||
Dept. of Computer Science,
|
|
||||||
Univ. of S\~ao Paulo,
|
|
||||||
S\~ao Paulo, Brazil\\
|
|
||||||
\email{yoshi@ime.usp.br}
|
|
||||||
}
|
|
||||||
|
|
||||||
\date{Received: date / Accepted: date}
|
|
||||||
% The correct dates will be entered by the editor
|
|
||||||
|
|
||||||
|
|
||||||
\maketitle
|
|
||||||
|
|
||||||
\begin{abstract}
|
|
||||||
Insert your abstract here. Include up to five keywords.
|
|
||||||
\keywords{First keyword \and Second keyword \and More}
|
|
||||||
\end{abstract}
|
|
||||||
|
|
||||||
% main text
|
|
||||||
\input{introduction}
|
|
||||||
\input{relatedwork}
|
|
||||||
\input{algorithms}
|
|
||||||
\input{experimentalresults}
|
|
||||||
\input{applications}
|
|
||||||
\input{conclusions}
|
|
||||||
|
|
||||||
|
|
||||||
%\begin{acknowledgements}
|
|
||||||
%If you'd like to thank anyone, place your comments here
|
|
||||||
%and remove the percent signs.
|
|
||||||
%\end{acknowledgements}
|
|
||||||
|
|
||||||
% BibTeX users please use
|
|
||||||
%\bibliographystyle{spmpsci}
|
|
||||||
%\bibliography{} % name your BibTeX data base
|
|
||||||
\bibliographystyle{plain}
|
|
||||||
\bibliography{references}
|
|
||||||
\end{document}
|
|
||||||
|
|
@ -1,19 +0,0 @@
|
||||||
\section{Os Algoritmos}
|
|
||||||
\label{sec:thealgorithm}
|
|
||||||
Nesta se\c{c}\~ao apresentamos \cite{bkz05}
|
|
||||||
\subsection{Um Algoritmo Baseado em Mem\'oria Principal}
|
|
||||||
|
|
||||||
\subsection{Um Algoritmo Baseado em Mem\'oria Externa}
|
|
||||||
% For two-column wide figures use
|
|
||||||
\begin{figure}
|
|
||||||
% Use the relevant command to insert your figure file.
|
|
||||||
% For example, with the graphicx package use
|
|
||||||
\centering
|
|
||||||
\includegraphics{figs/brz.ps}
|
|
||||||
% figure caption is below the figure
|
|
||||||
\caption{Main steps of the new algorithm.}
|
|
||||||
\label{fig:new-algo-main-steps}
|
|
||||||
\end{figure}
|
|
||||||
|
|
||||||
\subsubsection{Segmenta\c{c}\~ao}
|
|
||||||
\subsubsection{Espalhamento}
|
|
||||||
|
|
@ -1,2 +0,0 @@
|
||||||
\section{Aplica\c{c}\~oes}
|
|
||||||
\label{sec:applications}
|
|
||||||
|
|
@ -1,3 +0,0 @@
|
||||||
\section{Conclus\~oes}
|
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -1 +0,0 @@
|
||||||
\section{Resultados Experimentais}
|
|
||||||
|
|
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|
||||||
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4 -2 roll dup 1 exch sub 3 -1 roll mul add
|
|
||||||
4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
|
|
||||||
bind def
|
|
||||||
/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
|
|
||||||
4 -2 roll mul srgb} bind def
|
|
||||||
/reencdict 12 dict def /ReEncode { reencdict begin
|
|
||||||
/newcodesandnames exch def /newfontname exch def /basefontname exch def
|
|
||||||
/basefontdict basefontname findfont def /newfont basefontdict maxlength dict def
|
|
||||||
basefontdict { exch dup /FID ne { dup /Encoding eq
|
|
||||||
{ exch dup length array copy newfont 3 1 roll put }
|
|
||||||
{ exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall
|
|
||||||
newfont /FontName newfontname put newcodesandnames aload pop
|
|
||||||
128 1 255 { newfont /Encoding get exch /.notdef put } for
|
|
||||||
newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat
|
|
||||||
newfontname newfont definefont pop end } def
|
|
||||||
/isovec [
|
|
||||||
8#055 /minus 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde
|
|
||||||
8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis
|
|
||||||
8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron
|
|
||||||
8#220 /dotlessi 8#230 /oe 8#231 /OE
|
|
||||||
8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling
|
|
||||||
8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis
|
|
||||||
8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot
|
|
||||||
8#255 /hyphen 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus
|
|
||||||
8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph
|
|
||||||
8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine
|
|
||||||
8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf
|
|
||||||
8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute
|
|
||||||
8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring
|
|
||||||
8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute
|
|
||||||
8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute
|
|
||||||
8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve
|
|
||||||
8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply
|
|
||||||
8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex
|
|
||||||
8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave
|
|
||||||
8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring
|
|
||||||
8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute
|
|
||||||
8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute
|
|
||||||
8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve
|
|
||||||
8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide
|
|
||||||
8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex
|
|
||||||
8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def
|
|
||||||
/Times-Roman /Times-Roman-iso isovec ReEncode
|
|
||||||
/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
|
|
||||||
/$F2psEnd {$F2psEnteredState restore end} def
|
|
||||||
|
|
||||||
$F2psBegin
|
|
||||||
10 setmiterlimit
|
|
||||||
0 slj 0 slc
|
|
||||||
0.06299 0.06299 sc
|
|
||||||
%
|
|
||||||
% Fig objects follow
|
|
||||||
%
|
|
||||||
%
|
|
||||||
% here starts figure with depth 50
|
|
||||||
% Polyline
|
|
||||||
0 slj
|
|
||||||
0 slc
|
|
||||||
7.500 slw
|
|
||||||
n 3285 4140 m 3555 4140 l 3555 4230 l 3285 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 4050 m 3555 4050 l 3555 4140 l 3285 4140 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3960 m 3555 3960 l 3555 4050 l 3285 4050 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3870 m 3555 3870 l 3555 3960 l 3285 3960 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3780 m 3555 3780 l 3555 3870 l 3285 3870 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3690 m 3555 3690 l 3555 3780 l 3285 3780 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3600 m 3555 3600 l 3555 3690 l 3285 3690 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1800 4770 m 2070 4770 l 2070 4500 l 3060 4500 l 3060 4770 l 3330 4770 l
|
|
||||||
2565 5175 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
2265 4867 m
|
|
||||||
gs 1 -1 sc (Spreading) col0 sh gr
|
|
||||||
% Polyline
|
|
||||||
n 2250 3330 m 2430 3330 l 2430 3060 l 2700 3060 l 2700 3330 l 2880 3330 l
|
|
||||||
2565 3600 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
2521 3382 m
|
|
||||||
gs 1 -1 sc (h) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 95.25 scf sf
|
|
||||||
2589 3419 m
|
|
||||||
gs 1 -1 sc (1) col0 sh gr
|
|
||||||
% Polyline
|
|
||||||
n 1500 2655 m 1395 2655 1395 2865 105 arcto 4 {pop} repeat
|
|
||||||
1395 2970 3720 2970 105 arcto 4 {pop} repeat
|
|
||||||
3825 2970 3825 2760 105 arcto 4 {pop} repeat
|
|
||||||
3825 2655 1500 2655 105 arcto 4 {pop} repeat
|
|
||||||
cp gs col0 s gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
2212 2850 m
|
|
||||||
gs 1 -1 sc (Set of Keys S) col0 sh gr
|
|
||||||
% Polyline
|
|
||||||
n 1395 4230 m
|
|
||||||
3825 4230 l gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1395 4140 m 1665 4140 l 1665 4230 l 1395 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1395 4050 m 1665 4050 l 1665 4140 l 1395 4140 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1665 4140 m 1935 4140 l 1935 4230 l 1665 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1665 4050 m 1935 4050 l 1935 4140 l 1665 4140 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1665 3960 m 1935 3960 l 1935 4050 l 1665 4050 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1665 3870 m 1935 3870 l 1935 3960 l 1665 3960 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1665 3780 m 1935 3780 l 1935 3870 l 1665 3870 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2205 4140 m 2475 4140 l 2475 4230 l 2205 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2205 4050 m 2475 4050 l 2475 4140 l 2205 4140 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2205 3960 m 2475 3960 l 2475 4050 l 2205 4050 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2205 3870 m 2475 3870 l 2475 3960 l 2205 3960 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1665 3690 m 1935 3690 l 1935 3780 l 1665 3780 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2745 4140 m 3015 4140 l 3015 4230 l 2745 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3015 4140 m 3285 4140 l 3285 4230 l 3015 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2475 4140 m 2745 4140 l 2745 4230 l 2475 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2745 4050 m 3015 4050 l 3015 4140 l 2745 4140 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1395 3960 m 1665 3960 l 1665 4050 l 1395 4050 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3555 4140 m 3825 4140 l 3825 4230 l 3555 4230 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3555 4050 m 3825 4050 l 3825 4140 l 3555 4140 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3015 4050 m 3285 4050 l 3285 4140 l 3015 4140 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2745 3960 m 3015 3960 l 3015 4050 l 2745 4050 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2745 3870 m 3015 3870 l 3015 3960 l 2745 3960 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2745 3780 m 3015 3780 l 3015 3870 l 2745 3870 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1260 5400 m
|
|
||||||
4230 5400 l gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1530 5310 m 1800 5310 l 1800 5400 l 1530 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2070 5310 m 2340 5310 l 2340 5400 l 2070 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2340 5310 m 2610 5310 l 2610 5400 l 2340 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2610 5310 m 2880 5310 l 2880 5400 l 2610 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 2880 5310 m 3150 5310 l 3150 5400 l 2880 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3420 5310 m 3690 5310 l 3690 5400 l 3420 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3690 5310 m 3960 5310 l 3960 5400 l 3690 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3960 5310 m 4230 5310 l 4230 5400 l 3960 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1800 5310 m 2070 5310 l 2070 5400 l 1800 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3150 5310 m 3420 5310 l 3420 5400 l 3150 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 1260 5310 m 1530 5310 l 1530 5400 l 1260 5400 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3510 m 3555 3510 l 3555 3600 l 3285 3600 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n 3285 3420 m 3555 3420 l 3555 3510 l 3285 3510 l
|
|
||||||
cp gs col0 s gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
1485 4410 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
3600 4410 m
|
|
||||||
gs 1 -1 sc (b-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
720 4050 m
|
|
||||||
gs 1 -1 sc (Buckets) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
900 4230 m
|
|
||||||
gs 1 -1 sc (B) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
4005 5580 m
|
|
||||||
gs 1 -1 sc (n-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
1350 5580 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
450 5400 m
|
|
||||||
gs 1 -1 sc (Hash Table) col0 sh gr
|
|
||||||
% here ends figure;
|
|
||||||
$F2psEnd
|
|
||||||
rs
|
|
||||||
showpage
|
|
||||||
%%Trailer
|
|
||||||
%EOF
|
|
||||||
|
|
@ -1,206 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
6 2340 2970 4095 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3892.500 2047.500 2835 3825 3105 3960 3375 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 2677.500 3802.500 3330 3555 3375 3825 3330 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3523.500 4635.900 3375 4095 3060 4320 2970 4545
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3802.500 4567.500 3465 4050 3690 3960 3915 3960
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3686.786 4181.786 3915 4005 3960 4275 3780 4455
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3127.500 3802.500 3285 3555 2970 3555 2835 3825
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3127.500 4432.500 3375 4140 3510 4410 3420 4680
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 3220.500 4507.500 2970 4590 3195 4770 3420 4680
|
|
||||||
6 3825 3870 4050 4095
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3937 3982 94 92 3937 3982 3980 4067
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3900 4035 2\001
|
|
||||||
-6
|
|
||||||
6 3330 4545 3555 4770
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3442 4657 94 92 3442 4657 3485 4742
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3405 4710 4\001
|
|
||||||
-6
|
|
||||||
6 2880 4455 3105 4680
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 2992 4567 94 92 2992 4567 3035 4652
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 2955 4620 5\001
|
|
||||||
-6
|
|
||||||
6 2745 3690 2970 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 2857 3802 94 92 2857 3802 2900 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 2820 3855 7\001
|
|
||||||
-6
|
|
||||||
6 3195 3420 3420 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3307 3532 94 92 3307 3532 3350 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3270 3585 0\001
|
|
||||||
-6
|
|
||||||
6 3285 3960 3510 4185
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 3397 4072 94 92 3397 4072 3440 4157
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3360 4125 8\001
|
|
||||||
-6
|
|
||||||
6 2655 4050 2880 4275
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 2767 4162 94 92 2767 4162 2810 4247
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 2730 4215 6\001
|
|
||||||
-6
|
|
||||||
6 3600 3510 3825 3735
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 3712 3622 94 92 3712 3622 3755 3707
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3675 3675 1\001
|
|
||||||
-6
|
|
||||||
6 3690 4320 3915 4545
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 3802 4432 94 92 3802 4432 3845 4517
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3765 4485 3\001
|
|
||||||
-6
|
|
||||||
6 3285 2970 3465 3150
|
|
||||||
2 2 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 5
|
|
||||||
3285 2970 3465 2970 3465 3150 3285 3150 3285 2970
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 3337 3112 2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3645 3465 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 2430 4230 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 2655 4635 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3330 4905 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 2520 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3735 4680 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3870 3825 d:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3510 4185 d:5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 3240 3375 d:2\001
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 135 105 3060 3105 Q\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 2340 3105 b)\001
|
|
||||||
-6
|
|
||||||
6 450 2970 2115 4905
|
|
||||||
6 450 3240 2115 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1912.500 2047.500 855 3825 1125 3960 1395 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 697.500 3802.500 1350 3555 1395 3825 1350 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1543.500 4635.900 1395 4095 1080 4320 990 4545
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1822.500 4567.500 1485 4050 1710 3960 1935 3960
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1706.786 4181.786 1935 4005 1980 4275 1800 4455
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1147.500 3802.500 1305 3555 990 3555 855 3825
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1147.500 4432.500 1395 4140 1530 4410 1440 4680
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 1240.500 4507.500 990 4590 1215 4770 1440 4680
|
|
||||||
6 1845 3870 2070 4095
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1957 3982 94 92 1957 3982 2000 4067
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1920 4035 2\001
|
|
||||||
-6
|
|
||||||
6 1710 4320 1935 4545
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1822 4432 94 92 1822 4432 1865 4517
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1785 4485 3\001
|
|
||||||
-6
|
|
||||||
6 1350 4545 1575 4770
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1462 4657 94 92 1462 4657 1505 4742
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1425 4710 4\001
|
|
||||||
-6
|
|
||||||
6 900 4455 1125 4680
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1012 4567 94 92 1012 4567 1055 4652
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 975 4620 5\001
|
|
||||||
-6
|
|
||||||
6 765 3690 990 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 877 3802 94 92 877 3802 920 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 840 3855 7\001
|
|
||||||
-6
|
|
||||||
6 1215 3420 1440 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1327 3532 94 92 1327 3532 1370 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1290 3585 0\001
|
|
||||||
-6
|
|
||||||
6 1305 3960 1530 4185
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 1417 4072 94 92 1417 4072 1460 4157
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1380 4125 8\001
|
|
||||||
-6
|
|
||||||
6 675 4050 900 4275
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 787 4162 94 92 787 4162 830 4247
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 750 4215 6\001
|
|
||||||
-6
|
|
||||||
6 1620 3510 1845 3735
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 1732 3622 94 92 1732 3622 1775 3707
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1695 3675 1\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1665 3465 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 450 4230 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 675 4635 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1350 4905 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 540 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1755 4680 d:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1890 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1530 4185 d:5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 1260 3375 d:2\001
|
|
||||||
-6
|
|
||||||
6 1080 2970 1485 3150
|
|
||||||
6 1305 2970 1485 3150
|
|
||||||
2 2 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 5
|
|
||||||
1305 2970 1485 2970 1485 3150 1305 3150 1305 2970
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 1357 3112 3\001
|
|
||||||
-6
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 135 105 1080 3105 Q\001
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
6 4320 2970 6075 4905
|
|
||||||
6 4410 3015 6075 4905
|
|
||||||
6 5085 3015 5360 3156
|
|
||||||
6 5225 3015 5360 3150
|
|
||||||
1 1 0 1 0 33 45 -1 40 0.000 1 0.0000 5312 3080 44 52 5312 3080 5334 3125
|
|
||||||
2 1 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 2
|
|
||||||
5330 3020 5293 3141
|
|
||||||
-6
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 135 105 5085 3126 Q\001
|
|
||||||
-6
|
|
||||||
6 4410 3240 6075 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5872.500 2047.500 4815 3825 5085 3960 5355 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4657.500 3802.500 5310 3555 5355 3825 5310 4050
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5503.500 4635.900 5355 4095 5040 4320 4950 4545
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5782.500 4567.500 5445 4050 5670 3960 5895 3960
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5666.786 4181.786 5895 4005 5940 4275 5760 4455
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5107.500 3802.500 5265 3555 4950 3555 4815 3825
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5107.500 4432.500 5355 4140 5490 4410 5400 4680
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5200.500 4507.500 4950 4590 5175 4770 5400 4680
|
|
||||||
6 5310 4545 5535 4770
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5422 4657 94 92 5422 4657 5465 4742
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5385 4710 4\001
|
|
||||||
-6
|
|
||||||
6 4860 4455 5085 4680
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4972 4567 94 92 4972 4567 5015 4652
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4935 4620 5\001
|
|
||||||
-6
|
|
||||||
6 4725 3690 4950 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4837 3802 94 92 4837 3802 4880 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4800 3855 7\001
|
|
||||||
-6
|
|
||||||
6 5175 3420 5400 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5287 3532 94 92 5287 3532 5330 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5250 3585 0\001
|
|
||||||
-6
|
|
||||||
6 5265 3960 5490 4185
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5377 4072 94 92 5377 4072 5420 4157
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5340 4125 8\001
|
|
||||||
-6
|
|
||||||
6 4635 4050 4860 4275
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 4747 4162 94 92 4747 4162 4790 4247
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4710 4215 6\001
|
|
||||||
-6
|
|
||||||
6 5580 3510 5805 3735
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 5692 3622 94 92 5692 3622 5735 3707
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5655 3675 1\001
|
|
||||||
-6
|
|
||||||
6 5670 4320 5895 4545
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 5782 4432 94 92 5782 4432 5825 4517
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5745 4485 3\001
|
|
||||||
-6
|
|
||||||
6 5805 3870 6030 4095
|
|
||||||
1 1 0 1 0 7 45 -1 20 0.000 1 0.0000 5917 3982 94 92 5917 3982 5960 4067
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5880 4035 2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5625 3465 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 4410 4230 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 4635 4635 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5310 4905 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 4500 3825 d:2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5715 4680 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5850 3825 d:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5490 4185 d:4\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 195 5220 3375 d:2\001
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 3105 c)\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 360 3105 a)\001
|
|
||||||
|
|
@ -1,219 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
6 270 5220 1980 6615
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 855 5400 1080 5355 1305 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 967.500 5962.500 1620 5715 1665 5940 1620 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 1305 6480 1080 6525 855 6480
|
|
||||||
6 450 5625 630 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 5715 90 90 540 5715 630 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 510 5752 6\001
|
|
||||||
-6
|
|
||||||
6 765 5310 945 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 5400 90 90 855 5400 945 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 825 5437 7\001
|
|
||||||
-6
|
|
||||||
6 1215 5310 1395 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 5400 90 90 1305 5400 1395 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1275 5437 0\001
|
|
||||||
-6
|
|
||||||
6 1530 5625 1710 5805
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 5715 90 90 1620 5715 1710 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1590 5752 1\001
|
|
||||||
-6
|
|
||||||
6 1530 6075 1710 6255
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 6165 90 90 1620 6165 1710 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1590 6202 2\001
|
|
||||||
-6
|
|
||||||
6 1215 6390 1395 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 6480 90 90 1305 6480 1395 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1275 6517 3\001
|
|
||||||
-6
|
|
||||||
6 765 6390 945 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 6480 90 90 855 6480 945 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 825 6517 4\001
|
|
||||||
-6
|
|
||||||
6 450 6075 630 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 6165 90 90 540 6165 630 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 510 6202 5\001
|
|
||||||
-6
|
|
||||||
6 990 5850 1170 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1080 5940 90 90 1080 5940 1170 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1050 5977 8\001
|
|
||||||
-6
|
|
||||||
6 1665 5310 1980 5490
|
|
||||||
6 1800 5310 1980 5490
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1800 5310 1980 5310 1980 5490 1800 5490 1800 5310
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 1860 5437 2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 90 1665 5445 Q\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1620 5715
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 630 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 810 5985 d:5\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1395 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1755 5670 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1755 6255 d:1\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 1440 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 585 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 270 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 270 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 270 5355 a)\001
|
|
||||||
-6
|
|
||||||
6 4410 5220 6120 6615
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5220.000 5940.000 4995 5400 5220 5355 5445 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5107.500 5962.500 5760 5715 5805 5940 5760 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5220.000 5940.000 5445 6480 5220 6525 4995 6480
|
|
||||||
6 4590 5625 4770 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 5715 90 90 4680 5715 4770 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 5752 6\001
|
|
||||||
-6
|
|
||||||
6 4905 5310 5085 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4995 5400 90 90 4995 5400 5085 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4965 5437 7\001
|
|
||||||
-6
|
|
||||||
6 5355 5310 5535 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5445 5400 90 90 5445 5400 5535 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5415 5437 0\001
|
|
||||||
-6
|
|
||||||
6 5355 6390 5535 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5445 6480 90 90 5445 6480 5535 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5415 6517 3\001
|
|
||||||
-6
|
|
||||||
6 4905 6390 5085 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4995 6480 90 90 4995 6480 5085 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4965 6517 4\001
|
|
||||||
-6
|
|
||||||
6 4590 6075 4770 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 6165 90 90 4680 6165 4770 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 6202 5\001
|
|
||||||
-6
|
|
||||||
6 5130 5850 5310 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5220 5940 90 90 5220 5940 5310 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5190 5977 8\001
|
|
||||||
-6
|
|
||||||
6 5670 6075 5850 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 6165 90 90 5760 6165 5850 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 6202 2\001
|
|
||||||
-6
|
|
||||||
6 5670 5625 5850 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 5715 90 90 5760 5715 5850 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 5752 1\001
|
|
||||||
-6
|
|
||||||
6 5965 5332 6100 5467
|
|
||||||
1 1 0 1 0 33 45 -1 40 0.000 1 0.0000 6052 5397 44 52 6052 5397 6074 5442
|
|
||||||
2 1 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 2
|
|
||||||
6070 5337 6033 5458
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 5445 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 4995 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 5445 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 4995 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 5940 5760 5715
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5221 5943 5761 5718
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4770 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4950 5985 d:4\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5535 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5895 5670 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5895 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 5580 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4725 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4410 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 4410 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4410 5355 c)\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 90 5850 5445 Q\001
|
|
||||||
-6
|
|
||||||
6 2340 5220 4050 6615
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 2925 5400 3150 5355 3375 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3037.500 5962.500 3690 5715 3735 5940 3690 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 3375 6480 3150 6525 2925 6480
|
|
||||||
6 2520 5625 2700 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 5715 90 90 2610 5715 2700 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2580 5752 6\001
|
|
||||||
-6
|
|
||||||
6 2835 5310 3015 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 5400 90 90 2925 5400 3015 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2895 5437 7\001
|
|
||||||
-6
|
|
||||||
6 3285 5310 3465 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 5400 90 90 3375 5400 3465 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3345 5437 0\001
|
|
||||||
-6
|
|
||||||
6 3285 6390 3465 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 6480 90 90 3375 6480 3465 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3345 6517 3\001
|
|
||||||
-6
|
|
||||||
6 2835 6390 3015 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 6480 90 90 2925 6480 3015 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2895 6517 4\001
|
|
||||||
-6
|
|
||||||
6 2520 6075 2700 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 6165 90 90 2610 6165 2700 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2580 6202 5\001
|
|
||||||
-6
|
|
||||||
6 3060 5850 3240 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3150 5940 90 90 3150 5940 3240 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3120 5977 8\001
|
|
||||||
-6
|
|
||||||
6 3735 5310 4050 5490
|
|
||||||
6 3870 5310 4050 5490
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3870 5310 4050 5310 4050 5490 3870 5490 3870 5310
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 3930 5437 1\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 90 3735 5445 Q\001
|
|
||||||
-6
|
|
||||||
6 3600 5625 3780 5805
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3690 5715 90 90 3690 5715 3780 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3660 5752 1\001
|
|
||||||
-6
|
|
||||||
6 3600 6075 3780 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3690 6165 90 90 3690 6165 3780 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3660 6202 2\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3690 5715
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3151 5943 3691 5718
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2700 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2880 5985 d:5\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3465 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3825 5670 d:1\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3825 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 3510 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2655 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2340 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 150 2340 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 2340 5355 b)\001
|
|
||||||
-6
|
|
||||||
|
|
@ -1,130 +0,0 @@
|
||||||
#FIG 3.2
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d6d3d6
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 855 5400 1080 5355 1305 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 967.500 5962.500 1620 5715 1665 5940 1620 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1080.000 5940.000 1305 6480 1080 6525 855 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 2925 5400 3150 5355 3375 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3037.500 5962.500 3690 5715 3735 5940 3690 6210
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 3150.000 5940.000 3375 6480 3150 6525 2925 6480
|
|
||||||
6 450 5625 630 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 5715 90 90 540 5715 630 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 510 5752 6\001
|
|
||||||
-6
|
|
||||||
6 765 5310 945 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 5400 90 90 855 5400 945 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 825 5437 7\001
|
|
||||||
-6
|
|
||||||
6 1215 5310 1395 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 5400 90 90 1305 5400 1395 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1275 5437 0\001
|
|
||||||
-6
|
|
||||||
6 1530 5625 1710 5805
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 5715 90 90 1620 5715 1710 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1590 5752 1\001
|
|
||||||
-6
|
|
||||||
6 1530 6075 1710 6255
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1620 6165 90 90 1620 6165 1710 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1590 6202 2\001
|
|
||||||
-6
|
|
||||||
6 1215 6390 1395 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1305 6480 90 90 1305 6480 1395 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1275 6517 3\001
|
|
||||||
-6
|
|
||||||
6 765 6390 945 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 855 6480 90 90 855 6480 945 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 825 6517 4\001
|
|
||||||
-6
|
|
||||||
6 450 6075 630 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 540 6165 90 90 540 6165 630 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 510 6202 5\001
|
|
||||||
-6
|
|
||||||
6 990 5850 1170 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1080 5940 90 90 1080 5940 1170 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 1050 5977 8\001
|
|
||||||
-6
|
|
||||||
6 2520 5625 2700 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 5715 90 90 2610 5715 2700 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2580 5752 6\001
|
|
||||||
-6
|
|
||||||
6 2835 5310 3015 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 5400 90 90 2925 5400 3015 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2895 5437 7\001
|
|
||||||
-6
|
|
||||||
6 3285 5310 3465 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 5400 90 90 3375 5400 3465 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3345 5437 0\001
|
|
||||||
-6
|
|
||||||
6 3285 6390 3465 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3375 6480 90 90 3375 6480 3465 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3345 6517 3\001
|
|
||||||
-6
|
|
||||||
6 2835 6390 3015 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 2925 6480 90 90 2925 6480 3015 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2895 6517 4\001
|
|
||||||
-6
|
|
||||||
6 2520 6075 2700 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2610 6165 90 90 2610 6165 2700 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 2580 6202 5\001
|
|
||||||
-6
|
|
||||||
6 3060 5850 3240 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3150 5940 90 90 3150 5940 3240 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3120 5977 8\001
|
|
||||||
-6
|
|
||||||
6 3600 6075 3780 6255
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3690 6165 90 90 3690 6165 3780 6165
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3660 6202 2\001
|
|
||||||
-6
|
|
||||||
6 3600 5625 3780 5805
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3690 5715 90 90 3690 5715 3780 5715
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 60 3660 5752 1\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1305 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 855 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1080 5940 1620 5715
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3375 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 2925 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3150 5940 3690 5715
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3151 5943 3691 5718
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 630 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 810 5985 d:5\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1395 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1755 5670 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1755 6255 d:1\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 1440 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 585 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 270 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 270 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 150 135 270 5355 a)\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2700 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2880 5985 d:4\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3465 5310 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3825 5670 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3825 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3510 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2655 6615 d:2\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2340 5715 d:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2340 6255 d:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 150 150 2340 5355 b)\001
|
|
||||||
|
|
@ -1,168 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5692.500 1777.500 4635 3555 4905 3690 5175 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4477.500 3532.500 5130 3285 5175 3555 5130 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5323.500 4365.900 5175 3825 4860 4050 4770 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 4927.500 3532.500 5085 3285 4770 3285 4635 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4927.500 4162.500 5175 3870 5310 4140 5220 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 5020.500 4237.500 4770 4320 4995 4500 5220 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 10012.500 1777.500 8955 3555 9225 3690 9495 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 8797.500 3532.500 9450 3285 9495 3555 9450 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 9643.500 4365.900 9495 3825 9180 4050 9090 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 9247.500 3532.500 9405 3285 9090 3285 8955 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 9247.500 4162.500 9495 3870 9630 4140 9540 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 9340.500 4237.500 9090 4320 9315 4500 9540 4410
|
|
||||||
6 5130 4275 5355 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5242 4387 94 92 5242 4387 5285 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5205 4440 4\001
|
|
||||||
-6
|
|
||||||
6 4680 4185 4905 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4792 4297 94 92 4792 4297 4835 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4755 4350 5\001
|
|
||||||
-6
|
|
||||||
6 4545 3420 4770 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 4657 3532 94 92 4657 3532 4700 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 4620 3585 7\001
|
|
||||||
-6
|
|
||||||
6 5085 3690 5310 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5197 3802 94 92 5197 3802 5240 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5160 3855 8\001
|
|
||||||
-6
|
|
||||||
6 4995 3150 5220 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 5107 3262 94 92 5107 3262 5150 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 5070 3315 0\001
|
|
||||||
-6
|
|
||||||
6 7200 2970 8460 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 8572.500 1777.500 7515 3555 7785 3690 8055 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7357.500 3532.500 8010 3285 8055 3555 8010 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 8203.500 4365.900 8055 3825 7740 4050 7650 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 7807.500 3532.500 7965 3285 7650 3285 7515 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7807.500 4162.500 8055 3870 8190 4140 8100 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 7900.500 4237.500 7650 4320 7875 4500 8100 4410
|
|
||||||
6 7560 4185 7785 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 7672 4297 94 92 7672 4297 7715 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 7635 4350 5\001
|
|
||||||
-6
|
|
||||||
6 7425 3420 7650 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 7537 3532 94 92 7537 3532 7580 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 7500 3585 7\001
|
|
||||||
-6
|
|
||||||
6 7875 3150 8100 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 7987 3262 94 92 7987 3262 8030 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 7950 3315 0\001
|
|
||||||
-6
|
|
||||||
6 7965 3690 8190 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 8077 3802 94 92 8077 3802 8120 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 8040 3855 8\001
|
|
||||||
-6
|
|
||||||
6 8010 4275 8235 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 8122 4387 94 92 8122 4387 8165 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 8085 4440 4\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7553 4891 7733 4666
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7560 3825 7785 3645
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 7335 4365 g:3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 7200 3555 g:5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 7920 3105 g:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7560 3240 6\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7785 3645 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 8100 3555 1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 8235 4185 2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7740 4635 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 7650 4005 3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8235 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8010 4635 g:2\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 7200 3105 c)\001
|
|
||||||
-6
|
|
||||||
6 9000 4185 9225 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9112 4297 94 92 9112 4297 9155 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9075 4350 5\001
|
|
||||||
-6
|
|
||||||
6 8865 3420 9090 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 8977 3532 94 92 8977 3532 9020 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 8940 3585 7\001
|
|
||||||
-6
|
|
||||||
6 9315 3150 9540 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9427 3262 94 92 9427 3262 9470 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9390 3315 0\001
|
|
||||||
-6
|
|
||||||
6 9405 3690 9630 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9517 3802 94 92 9517 3802 9560 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9480 3855 8\001
|
|
||||||
-6
|
|
||||||
6 9450 4275 9675 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 9562 4387 94 92 9562 4387 9605 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 9525 4440 4\001
|
|
||||||
-6
|
|
||||||
6 5760 2835 7020 4905
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 7132.500 1777.500 6075 3555 6345 3690 6615 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5917.500 3532.500 6570 3285 6615 3555 6570 3780
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 6763.500 4365.900 6615 3825 6300 4050 6210 4275
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 6367.500 3532.500 6525 3285 6210 3285 6075 3555
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 6367.500 4162.500 6615 3870 6750 4140 6660 4410
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 0 6460.500 4237.500 6210 4320 6435 4500 6660 4410
|
|
||||||
6 6120 4185 6345 4410
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6232 4297 94 92 6232 4297 6275 4382
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6195 4350 5\001
|
|
||||||
-6
|
|
||||||
6 5985 3420 6210 3645
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6097 3532 94 92 6097 3532 6140 3617
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6060 3585 7\001
|
|
||||||
-6
|
|
||||||
6 6435 3150 6660 3375
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6547 3262 94 92 6547 3262 6590 3347
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6510 3315 0\001
|
|
||||||
-6
|
|
||||||
6 6525 3690 6750 3915
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6637 3802 94 92 6637 3802 6680 3887
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6600 3855 8\001
|
|
||||||
-6
|
|
||||||
6 6570 4275 6795 4500
|
|
||||||
1 1 0 1 0 33 45 -1 20 0.000 1 0.0000 6682 4387 94 92 6682 4387 6725 4472
|
|
||||||
4 0 0 45 -1 0 9 0.0000 4 105 75 6645 4440 4\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
6030 2835 6120 3105
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
6113 4891 6293 4666
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 5760 3105 b)\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 5895 4365 g:3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 5760 3555 g:4\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 6480 3105 g:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6120 3240 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6345 3645 4\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6660 3555 1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6795 4185 2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6300 4635 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 6210 4005 3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 6795 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 6570 4635 g:2\001
|
|
||||||
-6
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 5355 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 3105 a)\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8775 4365 g:3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 8640 3555 g:6\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 9360 3105 g:1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9000 3240 7\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9225 3645 6\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9540 3555 1\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9675 4185 2\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9180 4635 5\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 105 75 9090 4005 3\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 9675 3825 g:0\001
|
|
||||||
4 0 0 50 -1 0 9 0.0000 4 135 195 9450 4635 g:2\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 8640 3105 d)\001
|
|
||||||
|
|
@ -1,180 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 6210.000 5940.000 5985 5400 6210 5355 6435 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 6210.000 5940.000 6435 6480 6210 6525 5985 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7740.000 5940.000 7515 5400 7740 5355 7965 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 7740.000 5940.000 7965 6480 7740 6525 7515 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 9270.000 5940.000 9045 5400 9270 5355 9495 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 9270.000 5940.000 9495 6480 9270 6525 9045 6480
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4860.000 5940.000 4635 5400 4860 5355 5085 5400
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 4860.000 5940.000 5085 6480 4860 6525 4635 6480
|
|
||||||
6 5895 5310 6075 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5985 5400 90 90 5985 5400 6075 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5955 5437 7\001
|
|
||||||
-6
|
|
||||||
6 6345 5310 6525 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 6435 5400 90 90 6435 5400 6525 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6405 5437 0\001
|
|
||||||
-6
|
|
||||||
6 6345 6390 6525 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 6435 6480 90 90 6435 6480 6525 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6405 6517 3\001
|
|
||||||
-6
|
|
||||||
6 5895 6390 6075 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5985 6480 90 90 5985 6480 6075 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5955 6517 4\001
|
|
||||||
-6
|
|
||||||
6 6120 5850 6300 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 6210 5940 90 90 6210 5940 6300 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6180 5977 8\001
|
|
||||||
-6
|
|
||||||
6 7425 5310 7605 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7515 5400 90 90 7515 5400 7605 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7485 5437 7\001
|
|
||||||
-6
|
|
||||||
6 7875 5310 8055 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7965 5400 90 90 7965 5400 8055 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7935 5437 0\001
|
|
||||||
-6
|
|
||||||
6 7875 6390 8055 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7965 6480 90 90 7965 6480 8055 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7935 6517 3\001
|
|
||||||
-6
|
|
||||||
6 7425 6390 7605 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7515 6480 90 90 7515 6480 7605 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7485 6517 4\001
|
|
||||||
-6
|
|
||||||
6 7650 5850 7830 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 7740 5940 90 90 7740 5940 7830 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7710 5977 8\001
|
|
||||||
-6
|
|
||||||
6 8955 5310 9135 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9045 5400 90 90 9045 5400 9135 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9015 5437 7\001
|
|
||||||
-6
|
|
||||||
6 9405 5310 9585 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9495 5400 90 90 9495 5400 9585 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9465 5437 0\001
|
|
||||||
-6
|
|
||||||
6 9405 6390 9585 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9495 6480 90 90 9495 6480 9585 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9465 6517 3\001
|
|
||||||
-6
|
|
||||||
6 8955 6390 9135 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9045 6480 90 90 9045 6480 9135 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9015 6517 4\001
|
|
||||||
-6
|
|
||||||
6 9180 5850 9360 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 9270 5940 90 90 9270 5940 9360 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9240 5977 8\001
|
|
||||||
-6
|
|
||||||
6 4545 5310 4725 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4635 5400 90 90 4635 5400 4725 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4605 5437 7\001
|
|
||||||
-6
|
|
||||||
6 4995 5310 5175 5490
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5085 5400 90 90 5085 5400 5175 5400
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5055 5437 0\001
|
|
||||||
-6
|
|
||||||
6 4995 6390 5175 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5085 6480 90 90 5085 6480 5175 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5055 6517 3\001
|
|
||||||
-6
|
|
||||||
6 4545 6390 4725 6570
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4635 6480 90 90 4635 6480 4725 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4605 6517 4\001
|
|
||||||
-6
|
|
||||||
6 4770 5850 4950 6030
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 4860 5940 90 90 4860 5940 4950 5940
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4830 5977 8\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 6435 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 5985 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 6435 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
6210 5940 5985 6480
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 0 1 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
6255 5220 6615 5040
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
5760 6840 6120 6660
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7965 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7515 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7965 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
7740 5940 7515 6480
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7290 6840 7650 6660
|
|
||||||
2 1 0 1 0 7 45 -1 20 0.000 0 0 -1 1 0 2
|
|
||||||
1 1 1.00 60.00 120.00
|
|
||||||
7110 5895 7470 5715
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9495 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9045 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9495 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
9270 5940 9045 6480
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 5085 5400
|
|
||||||
2 1 0 1 0 7 50 -1 20 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 4635 5400
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 5085 6480
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
4860 5940 4635 6480
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 6345 5985 g:0\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 6570 5310 g:1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 5715 5310 g:4\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6165 5310 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5985 5715 4\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5985 6255 3\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6390 6255 2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6390 5715 1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 6165 6660 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 6525 6660 g:2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 5715 6660 g:3\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 5490 5445 b)\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 7875 5985 g:0\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8100 5310 g:1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 7245 5310 g:5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7695 5310 6\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7515 5715 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7515 6255 3\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7920 6255 2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7920 5715 1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 7695 6660 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8055 6660 g:2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 7245 6660 g:3\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 7020 5445 c)\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 9405 5985 g:0\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 9630 5310 g:1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8775 5310 g:6\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9225 5310 7\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9045 5715 6\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9045 6255 3\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9450 6255 2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9450 5715 1\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 9225 6660 5\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 9585 6660 g:2\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 8775 6660 g:3\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 8550 5445 d)\001
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 90 150 4995 5985 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 5445 a)\001
|
|
||||||
|
|
@ -1,124 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 33 #d3d3d3
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 1102.500 1462.500 1755 1215 1800 1440 1755 1710
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 2992.500 1462.500 3645 1215 3690 1440 3645 1710
|
|
||||||
5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 5107.500 1462.500 5760 1215 5805 1440 5760 1710
|
|
||||||
6 585 1125 765 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 675 1215 90 90 675 1215 765 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 645 1252 6\001
|
|
||||||
-6
|
|
||||||
6 585 1575 765 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 675 1665 90 90 675 1665 765 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 645 1702 5\001
|
|
||||||
-6
|
|
||||||
6 1125 1350 1305 1530
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 1215 1440 90 90 1215 1440 1305 1440
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1185 1477 8\001
|
|
||||||
-6
|
|
||||||
6 1665 1575 1845 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 1755 1665 90 90 1755 1665 1845 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1725 1702 2\001
|
|
||||||
-6
|
|
||||||
6 1665 1125 1845 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 1755 1215 90 90 1755 1215 1845 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 1725 1252 1\001
|
|
||||||
-6
|
|
||||||
6 1035 1890 1395 2070
|
|
||||||
6 1035 1890 1215 2070
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1035 1890 1215 1890 1215 2070 1035 2070 1035 1890
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 1095 2017 0\001
|
|
||||||
-6
|
|
||||||
6 1215 1890 1395 2070
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
1215 1890 1395 1890 1395 2070 1215 2070 1215 1890
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 1275 2017 4\001
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
6 2475 1125 2655 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2565 1215 90 90 2565 1215 2655 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2535 1252 6\001
|
|
||||||
-6
|
|
||||||
6 2475 1575 2655 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 2565 1665 90 90 2565 1665 2655 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 2535 1702 5\001
|
|
||||||
-6
|
|
||||||
6 3015 1350 3195 1530
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 3105 1440 90 90 3105 1440 3195 1440
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3075 1477 8\001
|
|
||||||
-6
|
|
||||||
6 3555 1575 3735 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3645 1665 90 90 3645 1665 3735 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3615 1702 2\001
|
|
||||||
-6
|
|
||||||
6 3555 1125 3735 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 3645 1215 90 90 3645 1215 3735 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 3615 1252 1\001
|
|
||||||
-6
|
|
||||||
6 3015 1890 3195 2070
|
|
||||||
2 2 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 5
|
|
||||||
3015 1890 3195 1890 3195 2070 3015 2070 3015 1890
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 3075 2017 4\001
|
|
||||||
-6
|
|
||||||
6 4590 1125 4770 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 1215 90 90 4680 1215 4770 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 1252 6\001
|
|
||||||
-6
|
|
||||||
6 4590 1575 4770 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 4680 1665 90 90 4680 1665 4770 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 4650 1702 5\001
|
|
||||||
-6
|
|
||||||
6 5130 1350 5310 1530
|
|
||||||
1 3 0 1 0 33 45 -1 20 0.000 1 0.0000 5220 1440 90 90 5220 1440 5310 1440
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5190 1477 8\001
|
|
||||||
-6
|
|
||||||
6 5670 1575 5850 1755
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 1665 90 90 5760 1665 5850 1665
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 1702 2\001
|
|
||||||
-6
|
|
||||||
6 5670 1125 5850 1305
|
|
||||||
1 3 0 1 0 7 45 -1 20 0.000 1 0.0000 5760 1215 90 90 5760 1215 5850 1215
|
|
||||||
4 0 0 45 -1 0 8 0.0000 4 75 60 5730 1252 1\001
|
|
||||||
-6
|
|
||||||
6 5130 1935 5265 2070
|
|
||||||
1 1 0 1 0 33 45 -1 40 0.000 1 0.0000 5217 2000 44 52 5217 2000 5239 2045
|
|
||||||
2 1 0 1 0 33 45 -1 40 0.000 0 0 7 0 0 2
|
|
||||||
5235 1940 5198 2061
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1215 1440 1755 1215
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
1216 1443 1756 1218
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3105 1440 3645 1215
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
3106 1443 3646 1218
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5220 1440 5760 1215
|
|
||||||
2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
|
|
||||||
5221 1443 5761 1218
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 945 1485 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 1110 630 2250 UnAssignedAddresses\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 2835 1485 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 3285 1305 0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 1110 2520 2250 UnAssignedAddresses\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 4950 1485 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 5400 1305 0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 105 1110 4635 2250 UnAssignedAddresses\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 4590 1890 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 5670 1890 g:4\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 5670 1080 g:0\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 4590 1080 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 4320 1125 c)\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 90 150 3555 1080 g:0\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 2205 1125 b)\001
|
|
||||||
4 0 0 50 -1 0 11 0.0000 4 180 165 315 1125 a)\001
|
|
||||||
4 0 0 50 -1 0 8 0.0000 4 75 60 5850 1485 4\001
|
|
||||||
|
|
@ -1,176 +0,0 @@
|
||||||
#FIG 3.2 Produced by xfig version 3.2.5-alpha5
|
|
||||||
Landscape
|
|
||||||
Center
|
|
||||||
Metric
|
|
||||||
A4
|
|
||||||
100.00
|
|
||||||
Single
|
|
||||||
-2
|
|
||||||
1200 2
|
|
||||||
0 32 #bebebe
|
|
||||||
6 -2700 3060 -540 3240
|
|
||||||
6 -2700 3060 -540 3240
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2700 3060 -2430 3060 -2430 3240 -2700 3240 -2700 3060
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2430 3060 -2160 3060 -2160 3240 -2430 3240 -2430 3060
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2160 3060 -1890 3060 -1890 3240 -2160 3240 -2160 3060
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1890 3060 -1620 3060 -1620 3240 -1890 3240 -1890 3060
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1620 3060 -1350 3060 -1350 3240 -1620 3240 -1620 3060
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1350 3060 -1080 3060 -1080 3240 -1350 3240 -1350 3060
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1080 3060 -810 3060 -810 3240 -1080 3240 -1080 3060
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-810 3060 -540 3060 -540 3240 -810 3240 -810 3060
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
6 -2610 2835 -540 2970
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2610 2970 0\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 210 -765 2970 n-1\001
|
|
||||||
4 0 0 45 -1 0 18 0.0000 4 30 180 -1575 2970 ...\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2070 2970 2\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2340 2970 1\001
|
|
||||||
-6
|
|
||||||
6 -3600 4230 270 5490
|
|
||||||
6 -2700 4455 -540 5265
|
|
||||||
6 -2700 4455 -540 4635
|
|
||||||
6 -2700 4455 -540 4635
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2700 4455 -2430 4455 -2430 4635 -2700 4635 -2700 4455
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2430 4455 -2160 4455 -2160 4635 -2430 4635 -2430 4455
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2160 4455 -1890 4455 -1890 4635 -2160 4635 -2160 4455
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1890 4455 -1620 4455 -1620 4635 -1890 4635 -1890 4455
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1620 4455 -1350 4455 -1350 4635 -1620 4635 -1620 4455
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1350 4455 -1080 4455 -1080 4635 -1350 4635 -1350 4455
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1080 4455 -810 4455 -810 4635 -1080 4635 -1080 4455
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-810 4455 -540 4455 -540 4635 -810 4635 -810 4455
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
6 -2700 5085 -540 5265
|
|
||||||
6 -2700 5085 -540 5265
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2700 5085 -2430 5085 -2430 5265 -2700 5265 -2700 5085
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2430 5085 -2160 5085 -2160 5265 -2430 5265 -2430 5085
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-2160 5085 -1890 5085 -1890 5265 -2160 5265 -2160 5085
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1890 5085 -1620 5085 -1620 5265 -1890 5265 -1890 5085
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1620 5085 -1350 5085 -1350 5265 -1620 5265 -1620 5085
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1350 5085 -1080 5085 -1080 5265 -1350 5265 -1350 5085
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1080 5085 -810 5085 -810 5265 -1080 5265 -1080 5085
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-810 5085 -540 5085 -540 5265 -810 5265 -810 5085
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
-6
|
|
||||||
6 -2610 4230 -540 4365
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2610 4365 0\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 210 -765 4365 n-1\001
|
|
||||||
4 0 0 45 -1 0 18 0.0000 4 30 180 -1575 4365 ...\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2070 4365 2\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2340 4365 1\001
|
|
||||||
-6
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-2565 4635 -1980 5085
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-2295 4635 -2565 5085
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-1980 4635 -2295 5085
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-1755 4635 -900 5085
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-1485 4635 -1755 5085
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-1215 4635 -1485 5085
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-675 4635 -1215 5085
|
|
||||||
2 1 0 1 0 0 45 -1 -1 0.000 0 0 -1 1 0 2
|
|
||||||
2 1 1.00 60.00 60.00
|
|
||||||
-945 4635 -675 5085
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 690 -450 5220 Hash Table\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 135 465 -450 4590 Key Set\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2610 5490 0\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 210 -765 5490 n-1\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2070 5490 2\001
|
|
||||||
4 0 0 45 -1 0 10 0.0000 4 105 75 -2340 5490 1\001
|
|
||||||
4 0 0 45 -1 0 18 0.0000 4 30 180 -1575 5445 ...\001
|
|
||||||
4 0 0 45 -1 0 11 0.0000 4 180 240 -3600 4860 (b)\001
|
|
||||||
-6
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1890 3690 -1620 3690 -1620 3870 -1890 3870 -1890 3690
|
|
||||||
2 2 0 1 0 7 45 -1 20 0.000 0 0 -1 0 0 5
|
|
||||||
-1350 3690 -1080 3690 -1080 3870 -1350 3870 -1350 3690
|
|
||||||
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|
||||||
-2073 5050 m -1986 5117 l -1949 5070 l -2037 5002 l -2037 5002 l -1996 5072 l -2073 5050 l cp
|
|
||||||
eoclip
|
|
||||||
n -2565 4635 m
|
|
||||||
-1980 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2073 5050 m -1996 5072 l -2037 5002 l -2043 5035 l -2073 5050 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2540 4987 m -2598 5082 l -2546 5113 l -2488 5018 l -2488 5018 l -2553 5067 l -2540 4987 l cp
|
|
||||||
eoclip
|
|
||||||
n -2295 4635 m
|
|
||||||
-2565 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2540 4987 m -2553 5067 l -2488 5018 l -2522 5015 l -2540 4987 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2263 4989 m -2328 5080 l -2279 5114 l -2214 5023 l -2214 5023 l -2282 5068 l -2263 4989 l cp
|
|
||||||
eoclip
|
|
||||||
n -1980 4635 m
|
|
||||||
-2295 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2263 4989 m -2282 5068 l -2214 5023 l -2247 5018 l -2263 4989 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-997 5066 m -900 5118 l -872 5065 l -969 5013 l -969 5013 l -917 5075 l -997 5066 l cp
|
|
||||||
eoclip
|
|
||||||
n -1755 4635 m
|
|
||||||
-900 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -997 5066 m -917 5075 l -969 5013 l -970 5047 l -997 5066 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1730 4987 m -1788 5082 l -1736 5113 l -1678 5018 l -1678 5018 l -1743 5067 l -1730 4987 l cp
|
|
||||||
eoclip
|
|
||||||
n -1485 4635 m
|
|
||||||
-1755 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1730 4987 m -1743 5067 l -1678 5018 l -1712 5015 l -1730 4987 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1460 4987 m -1518 5082 l -1466 5113 l -1408 5018 l -1408 5018 l -1473 5067 l -1460 4987 l cp
|
|
||||||
eoclip
|
|
||||||
n -1215 4635 m
|
|
||||||
-1485 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1460 4987 m -1473 5067 l -1408 5018 l -1442 5015 l -1460 4987 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1159 5000 m -1245 5071 l -1207 5117 l -1121 5047 l -1121 5047 l -1198 5072 l -1159 5000 l cp
|
|
||||||
eoclip
|
|
||||||
n -675 4635 m
|
|
||||||
-1215 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1159 5000 m -1198 5072 l -1121 5047 l -1151 5033 l -1159 5000 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-749 5018 m -693 5113 l -641 5082 l -697 4987 l -697 4987 l -685 5067 l -749 5018 l cp
|
|
||||||
eoclip
|
|
||||||
n -945 4635 m
|
|
||||||
-675 5085 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -749 5018 m -685 5067 l -697 4987 l -715 5015 l -749 5018 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-450 5220 m
|
|
||||||
gs 1 -1 sc (Hash Table) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-450 4590 m
|
|
||||||
gs 1 -1 sc (Key Set) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2610 5490 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-765 5490 m
|
|
||||||
gs 1 -1 sc (n-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2070 5490 m
|
|
||||||
gs 1 -1 sc (2) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2340 5490 m
|
|
||||||
gs 1 -1 sc (1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 285.75 scf sf
|
|
||||||
-1575 5445 m
|
|
||||||
gs 1 -1 sc (...) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 174.63 scf sf
|
|
||||||
-3600 4860 m
|
|
||||||
gs 1 -1 sc (\(b\)) col0 sh gr
|
|
||||||
% Polyline
|
|
||||||
n -1890 3690 m -1620 3690 l -1620 3870 l -1890 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1350 3690 m -1080 3690 l -1080 3870 l -1350 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1080 3690 m -810 3690 l -810 3870 l -1080 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -810 3690 m -540 3690 l -540 3870 l -810 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -3240 3690 m -2970 3690 l -2970 3870 l -3240 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -270 3690 m 0 3690 l 0 3870 l -270 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2970 3690 m -2700 3690 l -2700 3870 l -2970 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2700 3690 m -2430 3690 l -2430 3870 l -2700 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2430 3690 m -2160 3690 l -2160 3870 l -2430 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -1620 3690 m -1350 3690 l -1350 3870 l -1620 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -540 3690 m -270 3690 l -270 3870 l -540 3870 l
|
|
||||||
cp gs col32 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
n -2160 3690 m -1890 3690 l -1890 3870 l -2160 3870 l
|
|
||||||
cp gs col7 1.00 shd ef gr gs col0 s gr
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2116 3652 m -2032 3722 l -1994 3676 l -2078 3605 l -2078 3605 l -2040 3677 l -2116 3652 l cp
|
|
||||||
eoclip
|
|
||||||
n -2565 3240 m
|
|
||||||
-2025 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2116 3652 m -2040 3677 l -2078 3605 l -2086 3638 l -2116 3652 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-2540 3592 m -2598 3687 l -2546 3718 l -2488 3623 l -2488 3623 l -2553 3672 l -2540 3592 l cp
|
|
||||||
eoclip
|
|
||||||
n -2295 3240 m
|
|
||||||
-2565 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -2540 3592 m -2553 3672 l -2488 3623 l -2522 3620 l -2540 3592 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-3071 3626 m -3175 3667 l -3152 3723 l -3049 3682 l -3049 3682 l -3130 3682 l -3071 3626 l cp
|
|
||||||
eoclip
|
|
||||||
n -2025 3240 m
|
|
||||||
-3150 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -3071 3626 m -3130 3682 l -3049 3682 l -3074 3659 l -3071 3626 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1306 3652 m -1222 3722 l -1184 3676 l -1268 3605 l -1268 3605 l -1230 3677 l -1306 3652 l cp
|
|
||||||
eoclip
|
|
||||||
n -1755 3240 m
|
|
||||||
-1215 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1306 3652 m -1230 3677 l -1268 3605 l -1276 3638 l -1306 3652 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-1730 3592 m -1788 3687 l -1736 3718 l -1678 3623 l -1678 3623 l -1743 3672 l -1730 3592 l cp
|
|
||||||
eoclip
|
|
||||||
n -1485 3240 m
|
|
||||||
-1755 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -1730 3592 m -1743 3672 l -1678 3623 l -1712 3620 l -1730 3592 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-188 3682 m -87 3723 l -64 3667 l -166 3626 l -166 3626 l -108 3682 l -188 3682 l cp
|
|
||||||
eoclip
|
|
||||||
n -1215 3240 m
|
|
||||||
-90 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -188 3682 m -108 3682 l -166 3626 l -163 3659 l -188 3682 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-920 3592 m -978 3687 l -926 3718 l -868 3623 l -868 3623 l -933 3672 l -920 3592 l cp
|
|
||||||
eoclip
|
|
||||||
n -675 3240 m
|
|
||||||
-945 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -920 3592 m -933 3672 l -868 3623 l -902 3620 l -920 3592 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
% Polyline
|
|
||||||
gs clippath
|
|
||||||
-749 3623 m -693 3718 l -641 3687 l -697 3592 l -697 3592 l -685 3672 l -749 3623 l cp
|
|
||||||
eoclip
|
|
||||||
n -945 3240 m
|
|
||||||
-675 3690 l gs col0 s gr gr
|
|
||||||
|
|
||||||
% arrowhead
|
|
||||||
n -749 3623 m -685 3672 l -697 3592 l -715 3620 l -749 3623 l
|
|
||||||
cp gs 0.00 setgray ef gr col0 s
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2610 4095 m
|
|
||||||
gs 1 -1 sc (2) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-2880 4095 m
|
|
||||||
gs 1 -1 sc (1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-3150 4095 m
|
|
||||||
gs 1 -1 sc (0) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 285.75 scf sf
|
|
||||||
-1575 4050 m
|
|
||||||
gs 1 -1 sc (...) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-270 4095 m
|
|
||||||
gs 1 -1 sc (m-1) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
-450 3195 m
|
|
||||||
gs 1 -1 sc (Key Set) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 158.75 scf sf
|
|
||||||
90 3825 m
|
|
||||||
gs 1 -1 sc (Hash Table) col0 sh gr
|
|
||||||
/Times-Roman-iso ff 174.63 scf sf
|
|
||||||
-3600 3465 m
|
|
||||||
gs 1 -1 sc (\(a\)) col0 sh gr
|
|
||||||
% here ends figure;
|
|
||||||
$F2psEnd
|
|
||||||
rs
|
|
||||||
showpage
|
|
||||||
%%Trailer
|
|
||||||
%EOF
|
|
||||||
|
|
@ -1,55 +0,0 @@
|
||||||
\section{Introdu\c{c}\~ao}
|
|
||||||
\label{sec:introduction}
|
|
||||||
Fun\c{c}\~oes hash s\~ao amplamente utilizadas em v\'arias \'areas da
|
|
||||||
Ci\^encia da Computa\c{c}\~ao.
|
|
||||||
Uma \textit{fun\c{c}\~ao hash} $h: U \to M$ mapeia chaves de um universo $U$, $|U|=u$,
|
|
||||||
para um dado intervalo de inteiros $M=[0,m-1]=\{0,1,\dots,m-1\}$.
|
|
||||||
Seja~$S\subseteq U$ um subconjunto de $n$ chaves do universo $U$.
|
|
||||||
Dado uma chave~$k\in S$, uma fun\c{c}\~ao hash $h$ computa um inteiro em
|
|
||||||
$M$ para armazenamento ou recupera\c{c}\~ao de $k$ em uma \textit{tabela hash}.
|
|
||||||
Neste artigo consideramos que as chaves s\~ao strings de bits de comprimento
|
|
||||||
m\'aximo $L$. Portanto $u = 2^L$.
|
|
||||||
|
|
||||||
M\'etodos de hashing para {\em conjuntos n\~ao est\'aticos} de chaves podem ser usados para
|
|
||||||
construir estruturas de dados para armazenar $S$ e suportar consultas do tipo
|
|
||||||
``$k \in S$?'' em tempo esperado $O(1)$.
|
|
||||||
No entanto, eles envolvem um certo desperd\'{\i}cio de espa\c{c}o e tempo devido
|
|
||||||
a localiza\c{c}\~oes inutilizadas na tabela e tempo para resolver colis\~oes quando duas
|
|
||||||
chaves s\~ao mapeadas para a mesma localiza\c{c}\~ao na tabela.
|
|
||||||
|
|
||||||
|
|
||||||
Para {\em conjuntos est\'aticos} de chaves \'e poss\'{\i}vel computar uma fun\c{c}\~ao
|
|
||||||
para encontrar qualquer chave na tabela em uma \'unica tentativa; tais fun\c{c}\~oes
|
|
||||||
s\~ao chamadas de \textit{perfeitas}.
|
|
||||||
Dado um conjunto de chaves $S$, dizemos que uma fun\c{c}\~ao hash $h:U\to M$ \'e uma
|
|
||||||
\textit{fun\c{c}\~ao hash perfeita} (FHP) para $S$ se $h$ \'e injetora para $S$,
|
|
||||||
isto \'e, n\~ao h\'a {\em colis\~oes} entre as chaves em $S$: se $x$
|
|
||||||
e $y$ est\~ao em $S$ e $x\neq y$, ent\~ao $h(x)\neq h(y)$.
|
|
||||||
A Figura~\ref{fig:minimalperfecthash-ph-mph}(a) ilustra uma fun\c{c}\~ao hash perfeita.
|
|
||||||
Se $m=n$, isto \'e, a tabela \'e do mesmo tamanho de $S$,
|
|
||||||
ent\~ao $h$ \'e uma \textit{fun\c{c}\~ao hash perfeita m\'{\i}nima} (FHPM).
|
|
||||||
A Figura~\ref{fig:minimalperfecthash-ph-mph}(b) ilustra uma
|
|
||||||
fun\c{c}\~ao hash perfeita m\'{\i}nima.
|
|
||||||
FHPMs podem evitar totalmente o problema de desperd\'{\i}cio de espa\c{c}o e tempo.
|
|
||||||
|
|
||||||
% For two-column wide figures use
|
|
||||||
\begin{figure}
|
|
||||||
% Use the relevant command to insert your figure file.
|
|
||||||
% For example, with the graphicx package use
|
|
||||||
\centering
|
|
||||||
\includegraphics[width=0.45\textwidth, height=0.3\textheight]{figs/minimalperfecthash-ph-mph.ps}
|
|
||||||
% figure caption is below the figure
|
|
||||||
\caption{(a) Perfect hash function\quad (b) Minimal perfect hash function}
|
|
||||||
\label{fig:minimalperfecthash-ph-mph}
|
|
||||||
\end{figure}
|
|
||||||
|
|
||||||
A aplicabilidade pr\'atica das FHPMs e consequentemente dos algoritmos utilizados para ger\'a-las est\'a diretamente relacionada com as seguintes m\'etricas:
|
|
||||||
\begin{enumerate}
|
|
||||||
\item Quantidade de tempo gasto para encontrar uma FHPM $h$.
|
|
||||||
\item Quantidade de mem\'oria exigida para encontrar $h$.
|
|
||||||
\item Quantidade de tempo necess\'ario para avaliar ou computar $h$ para uma dada chave.
|
|
||||||
\item Quantidade de mem\'oria exigida para armazenar a descri\c{c}\~ao da fun\c{c}\~ao $h$.
|
|
||||||
\item Escalabilidade dos algoritmos com o crescimento de $S$.
|
|
||||||
\end{enumerate}
|
|
||||||
|
|
||||||
Neste artigo apresentamos ...
|
|
||||||
|
|
@ -1,17 +0,0 @@
|
||||||
all:
|
|
||||||
latex vldb.tex
|
|
||||||
bibtex vldb
|
|
||||||
latex vldb.tex
|
|
||||||
latex vldb.tex
|
|
||||||
dvips vldb.dvi -o vldb.ps
|
|
||||||
ps2pdf vldb.ps
|
|
||||||
chmod -R g+rwx *
|
|
||||||
|
|
||||||
perm:
|
|
||||||
chmod -R g+rwx *
|
|
||||||
|
|
||||||
run: clean all
|
|
||||||
gv vldb.ps &
|
|
||||||
clean:
|
|
||||||
rm *.aux *.bbl *.blg *.log
|
|
||||||
|
|
||||||
|
|
@ -1,700 +0,0 @@
|
||||||
@inproceedings{p99,
|
|
||||||
author = {R. Pagh},
|
|
||||||
title = {Hash and Displace: Efficient Evaluation of Minimal Perfect Hash Functions},
|
|
||||||
booktitle = {Workshop on Algorithms and Data Structures},
|
|
||||||
pages = {49-54},
|
|
||||||
year = 1999,
|
|
||||||
url = {citeseer.nj.nec.com/pagh99hash.html},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{p00,
|
|
||||||
author = {R. Pagh},
|
|
||||||
title = {Faster deterministic dictionaries},
|
|
||||||
journal = {Symposium on Discrete Algorithms (ACM SODA)},
|
|
||||||
OPTvolume = {43},
|
|
||||||
OPTnumber = {5},
|
|
||||||
pages = {487--493},
|
|
||||||
year = {2000}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{gss01,
|
|
||||||
author = {N. Galli and B. Seybold and K. Simon},
|
|
||||||
title = {Tetris-Hashing or optimal table compression},
|
|
||||||
journal = {Discrete Applied Mathematics},
|
|
||||||
volume = {110},
|
|
||||||
number = {1},
|
|
||||||
pages = {41--58},
|
|
||||||
month = {june},
|
|
||||||
publisher = {Elsevier Science},
|
|
||||||
year = {2001}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@InProceedings{ss89,
|
|
||||||
author = {P. Schmidt and A. Siegel},
|
|
||||||
title = {On aspects of universality and performance for closed hashing},
|
|
||||||
booktitle = {Proc. 21th Ann. ACM Symp. on Theory of Computing -- STOC'89},
|
|
||||||
month = {May},
|
|
||||||
year = {1989},
|
|
||||||
pages = {355--366}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{asw00,
|
|
||||||
author = {M. Atici and D. R. Stinson and R. Wei.},
|
|
||||||
title = {A new practical algorithm for the construction of a perfect hash function},
|
|
||||||
journal = {Journal Combin. Math. Combin. Comput.},
|
|
||||||
volume = {35},
|
|
||||||
pages = {127--145},
|
|
||||||
year = {2000}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{swz00,
|
|
||||||
author = {D. R. Stinson and R. Wei and L. Zhu},
|
|
||||||
title = {New constructions for perfect hash families and related structures using combinatorial designs and codes},
|
|
||||||
journal = {Journal Combin. Designs.},
|
|
||||||
volume = {8},
|
|
||||||
pages = {189--200},
|
|
||||||
year = {2000}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{ht01,
|
|
||||||
author = {T. Hagerup and T. Tholey},
|
|
||||||
title = {Efficient minimal perfect hashing in nearly minimal space},
|
|
||||||
booktitle = {The 18th Symposium on Theoretical Aspects of Computer Science (STACS), volume 2010 of Lecture Notes in Computer Science},
|
|
||||||
year = 2001,
|
|
||||||
pages = {317--326},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{dh01,
|
|
||||||
author = {M. Dietzfelbinger and T. Hagerup},
|
|
||||||
title = {Simple minimal perfect hashing in less space},
|
|
||||||
booktitle = {The 9th European Symposium on Algorithms (ESA), volume 2161 of Lecture Notes in Computer Science},
|
|
||||||
year = 2001,
|
|
||||||
pages = {109--120},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@MastersThesis{mar00,
|
|
||||||
author = {M. S. Neubert},
|
|
||||||
title = {Algoritmos Distribu<62>os para a Constru<72>o de Arquivos invertidos},
|
|
||||||
school = {Departamento de Ci<43>cia da Computa<74>o, Universidade Federal de Minas Gerais},
|
|
||||||
year = 2000,
|
|
||||||
month = {Mar<61>},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{clrs01,
|
|
||||||
author = {T. H. Cormen and C. E. Leiserson and R. L. Rivest and C. Stein},
|
|
||||||
title = {Introduction to Algorithms},
|
|
||||||
publisher = {MIT Press},
|
|
||||||
year = {2001},
|
|
||||||
edition = {second},
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{k73,
|
|
||||||
author = {D. E. Knuth},
|
|
||||||
title = {The Art of Computer Programming: Sorting and Searching},
|
|
||||||
publisher = {Addison-Wesley},
|
|
||||||
volume = {3},
|
|
||||||
year = {1973},
|
|
||||||
edition = {second},
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{rp99,
|
|
||||||
author = {R. Pagh},
|
|
||||||
title = {Hash and Displace: Efficient Evaluation of Minimal Perfect Hash Functions},
|
|
||||||
booktitle = {Workshop on Algorithms and Data Structures},
|
|
||||||
pages = {49-54},
|
|
||||||
year = 1999,
|
|
||||||
url = {citeseer.nj.nec.com/pagh99hash.html},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{hmwc93,
|
|
||||||
author = {G. Havas and B.S. Majewski and N.C. Wormald and Z.J. Czech},
|
|
||||||
title = {Graphs, Hypergraphs and Hashing},
|
|
||||||
booktitle = {19th International Workshop on Graph-Theoretic Concepts in Computer Science},
|
|
||||||
publisher = {Springer Lecture Notes in Computer Science vol. 790},
|
|
||||||
pages = {153-165},
|
|
||||||
year = 1993,
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{bkz05,
|
|
||||||
author = {F.C. Botelho and Y. Kohayakawa and N. Ziviani},
|
|
||||||
title = {A Practical Minimal Perfect Hashing Method},
|
|
||||||
booktitle = {4th International Workshop on Efficient and Experimental Algorithms},
|
|
||||||
publisher = {Springer Lecture Notes in Computer Science vol. 3503},
|
|
||||||
pages = {488-500},
|
|
||||||
Moth = May,
|
|
||||||
year = 2005,
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{chm97,
|
|
||||||
author = {Z.J. Czech and G. Havas and B.S. Majewski},
|
|
||||||
title = {Fundamental Study Perfect Hashing},
|
|
||||||
journal = {Theoretical Computer Science},
|
|
||||||
volume = {182},
|
|
||||||
year = {1997},
|
|
||||||
pages = {1-143},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{chm92,
|
|
||||||
author = {Z.J. Czech and G. Havas and B.S. Majewski},
|
|
||||||
title = {An Optimal Algorithm for Generating Minimal Perfect Hash Functions},
|
|
||||||
journal = {Information Processing Letters},
|
|
||||||
volume = {43},
|
|
||||||
number = {5},
|
|
||||||
pages = {257-264},
|
|
||||||
year = {1992},
|
|
||||||
url = {citeseer.nj.nec.com/czech92optimal.html},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{mwhc96,
|
|
||||||
author = {B.S. Majewski and N.C. Wormald and G. Havas and Z.J. Czech},
|
|
||||||
title = {A family of perfect hashing methods},
|
|
||||||
journal = {The Computer Journal},
|
|
||||||
year = {1996},
|
|
||||||
volume = {39},
|
|
||||||
number = {6},
|
|
||||||
pages = {547-554},
|
|
||||||
key = {author}
|
|
||||||
}
|
|
||||||
|
|
||||||
@InProceedings{bv04,
|
|
||||||
author = {P. Boldi and S. Vigna},
|
|
||||||
title = {The WebGraph Framework I: Compression Techniques},
|
|
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booktitle = {13th International World Wide Web Conference},
|
|
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pages = {595--602},
|
|
||||||
year = {2004}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{z04,
|
|
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author = {N. Ziviani},
|
|
||||||
title = {Projeto de Algoritmos com implementa<74>es em Pascal e C},
|
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publisher = {Pioneira Thompson},
|
|
||||||
year = 2004,
|
|
||||||
edition = {segunda edi<64>o}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Book{p85,
|
|
||||||
author = {E. M. Palmer},
|
|
||||||
title = {Graphical Evolution: An Introduction to the Theory of Random Graphs},
|
|
||||||
publisher = {John Wiley \& Sons},
|
|
||||||
year = {1985},
|
|
||||||
address = {New York}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Book{imb99,
|
|
||||||
author = {I.H. Witten and A. Moffat and T.C. Bell},
|
|
||||||
title = {Managing Gigabytes: Compressing and Indexing Documents and Images},
|
|
||||||
publisher = {Morgan Kaufmann Publishers},
|
|
||||||
year = 1999,
|
|
||||||
edition = {second edition}
|
|
||||||
}
|
|
||||||
@Book{wfe68,
|
|
||||||
author = {W. Feller},
|
|
||||||
title = { An Introduction to Probability Theory and Its Applications},
|
|
||||||
publisher = {Wiley},
|
|
||||||
year = 1968,
|
|
||||||
volume = 1,
|
|
||||||
optedition = {second edition}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Article{fhcd92,
|
|
||||||
author = {E.A. Fox and L. S. Heath and Q.Chen and A.M. Daoud},
|
|
||||||
title = {Practical Minimal Perfect Hash Functions For Large Databases},
|
|
||||||
journal = {Communications of the ACM},
|
|
||||||
year = {1992},
|
|
||||||
volume = {35},
|
|
||||||
number = {1},
|
|
||||||
pages = {105--121}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@inproceedings{fch92,
|
|
||||||
author = {E.A. Fox and Q.F. Chen and L.S. Heath},
|
|
||||||
title = {A Faster Algorithm for Constructing Minimal Perfect Hash Functions},
|
|
||||||
booktitle = {Proceedings of the 15th Annual International ACM SIGIR Conference
|
|
||||||
on Research and Development in Information Retrieval},
|
|
||||||
year = {1992},
|
|
||||||
pages = {266-273},
|
|
||||||
}
|
|
||||||
|
|
||||||
@article{c80,
|
|
||||||
author = {R.J. Cichelli},
|
|
||||||
title = {Minimal perfect hash functions made simple},
|
|
||||||
journal = {Communications of the ACM},
|
|
||||||
volume = {23},
|
|
||||||
number = {1},
|
|
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year = {1980},
|
|
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issn = {0001-0782},
|
|
||||||
pages = {17--19},
|
|
||||||
doi = {http://doi.acm.org/10.1145/358808.358813},
|
|
||||||
publisher = {ACM Press},
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@TechReport{fhc89,
|
|
||||||
author = {E.A. Fox and L.S. Heath and Q.F. Chen},
|
|
||||||
title = {An $O(n\log n)$ algorithm for finding minimal perfect hash functions},
|
|
||||||
institution = {Virginia Polytechnic Institute and State University},
|
|
||||||
year = {1989},
|
|
||||||
OPTkey = {},
|
|
||||||
OPTtype = {},
|
|
||||||
OPTnumber = {},
|
|
||||||
address = {Blacksburg, VA},
|
|
||||||
month = {April},
|
|
||||||
OPTnote = {},
|
|
||||||
OPTannote = {}
|
|
||||||
}
|
|
||||||
|
|
||||||
@inproceedings{fcdh90,
|
|
||||||
author = {E.A. Fox and Q.F. Chen and A.M. Daoud and L.S. Heath},
|
|
||||||
title = {Order preserving minimal perfect hash functions and information retrieval},
|
|
||||||
booktitle = {Proceedings of the 13th annual international ACM SIGIR conference on Research and development in information retrieval},
|
|
||||||
year = {1990},
|
|
||||||
isbn = {0-89791-408-2},
|
|
||||||
pages = {279--311},
|
|
||||||
location = {Brussels, Belgium},
|
|
||||||
doi = {http://doi.acm.org/10.1145/96749.98233},
|
|
||||||
publisher = {ACM Press},
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{fkp89,
|
|
||||||
author = {P. Flajolet and D. E. Knuth and B. Pittel},
|
|
||||||
title = {The first cycles in an evolving graph},
|
|
||||||
journal = {Discrete Math},
|
|
||||||
year = {1989},
|
|
||||||
volume = {75},
|
|
||||||
pages = {167-215},
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{s77,
|
|
||||||
author = {R. Sprugnoli},
|
|
||||||
title = {Perfect Hashing Functions: A Single Probe Retrieving
|
|
||||||
Method For Static Sets},
|
|
||||||
journal = {Communications of the ACM},
|
|
||||||
year = {1977},
|
|
||||||
volume = {20},
|
|
||||||
number = {11},
|
|
||||||
pages = {841--850},
|
|
||||||
month = {November},
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{j81,
|
|
||||||
author = {G. Jaeschke},
|
|
||||||
title = {Reciprocal Hashing: A method For Generating Minimal Perfect
|
|
||||||
Hashing Functions},
|
|
||||||
journal = {Communications of the ACM},
|
|
||||||
year = {1981},
|
|
||||||
volume = {24},
|
|
||||||
number = {12},
|
|
||||||
month = {December},
|
|
||||||
pages = {829--833}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{c84,
|
|
||||||
author = {C. C. Chang},
|
|
||||||
title = {The Study Of An Ordered Minimal Perfect Hashing Scheme},
|
|
||||||
journal = {Communications of the ACM},
|
|
||||||
year = {1984},
|
|
||||||
volume = {27},
|
|
||||||
number = {4},
|
|
||||||
month = {December},
|
|
||||||
pages = {384--387}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{c86,
|
|
||||||
author = {C. C. Chang},
|
|
||||||
title = {Letter-Oriented Reciprocal Hashing Scheme},
|
|
||||||
journal = {Inform. Sci.},
|
|
||||||
year = {1986},
|
|
||||||
volume = {27},
|
|
||||||
pages = {243--255}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{cl86,
|
|
||||||
author = {C. C. Chang and R. C. T. Lee},
|
|
||||||
title = {A Letter-Oriented Minimal Perfect Hashing Scheme},
|
|
||||||
journal = {Computer Journal},
|
|
||||||
year = {1986},
|
|
||||||
volume = {29},
|
|
||||||
number = {3},
|
|
||||||
month = {June},
|
|
||||||
pages = {277--281}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Article{cc88,
|
|
||||||
author = {C. C. Chang and C. H. Chang},
|
|
||||||
title = {An Ordered Minimal Perfect Hashing Scheme with Single Parameter},
|
|
||||||
journal = {Inform. Process. Lett.},
|
|
||||||
year = {1988},
|
|
||||||
volume = {27},
|
|
||||||
number = {2},
|
|
||||||
month = {February},
|
|
||||||
pages = {79--83}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{w90,
|
|
||||||
author = {V. G. Winters},
|
|
||||||
title = {Minimal Perfect Hashing in Polynomial Time},
|
|
||||||
journal = {BIT},
|
|
||||||
year = {1990},
|
|
||||||
volume = {30},
|
|
||||||
number = {2},
|
|
||||||
pages = {235--244}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{fcdh91,
|
|
||||||
author = {E. A. Fox and Q. F. Chen and A. M. Daoud and L. S. Heath},
|
|
||||||
title = {Order Preserving Minimal Perfect Hash Functions and Information Retrieval},
|
|
||||||
journal = {ACM Trans. Inform. Systems},
|
|
||||||
year = {1991},
|
|
||||||
volume = {9},
|
|
||||||
number = {3},
|
|
||||||
month = {July},
|
|
||||||
pages = {281--308}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{fks84,
|
|
||||||
author = {M. L. Fredman and J. Koml\'os and E. Szemer\'edi},
|
|
||||||
title = {Storing a sparse table with {O(1)} worst case access time},
|
|
||||||
journal = {J. ACM},
|
|
||||||
year = {1984},
|
|
||||||
volume = {31},
|
|
||||||
number = {3},
|
|
||||||
month = {July},
|
|
||||||
pages = {538--544}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{dhjs83,
|
|
||||||
author = {M. W. Du and T. M. Hsieh and K. F. Jea and D. W. Shieh},
|
|
||||||
title = {The study of a new perfect hash scheme},
|
|
||||||
journal = {IEEE Trans. Software Eng.},
|
|
||||||
year = {1983},
|
|
||||||
volume = {9},
|
|
||||||
number = {3},
|
|
||||||
month = {May},
|
|
||||||
pages = {305--313}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{bt94,
|
|
||||||
author = {M. D. Brain and A. L. Tharp},
|
|
||||||
title = {Using Tries to Eliminate Pattern Collisions in Perfect Hashing},
|
|
||||||
journal = {IEEE Trans. on Knowledge and Data Eng.},
|
|
||||||
year = {1994},
|
|
||||||
volume = {6},
|
|
||||||
number = {2},
|
|
||||||
month = {April},
|
|
||||||
pages = {239--247}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{bt90,
|
|
||||||
author = {M. D. Brain and A. L. Tharp},
|
|
||||||
title = {Perfect hashing using sparse matrix packing},
|
|
||||||
journal = {Inform. Systems},
|
|
||||||
year = {1990},
|
|
||||||
volume = {15},
|
|
||||||
number = {3},
|
|
||||||
OPTmonth = {April},
|
|
||||||
pages = {281--290}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{ckw93,
|
|
||||||
author = {C. C. Chang and H. C.Kowng and T. C. Wu},
|
|
||||||
title = {A refinement of a compression-oriented addressing scheme},
|
|
||||||
journal = {BIT},
|
|
||||||
year = {1993},
|
|
||||||
volume = {33},
|
|
||||||
number = {4},
|
|
||||||
OPTmonth = {April},
|
|
||||||
pages = {530--535}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{cw91,
|
|
||||||
author = {C. C. Chang and T. C. Wu},
|
|
||||||
title = {A letter-oriented perfect hashing scheme based upon sparse table compression},
|
|
||||||
journal = {Software -- Practice Experience},
|
|
||||||
year = {1991},
|
|
||||||
volume = {21},
|
|
||||||
number = {1},
|
|
||||||
month = {january},
|
|
||||||
pages = {35--49}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{ty79,
|
|
||||||
author = {R. E. Tarjan and A. C. C. Yao},
|
|
||||||
title = {Storing a sparse table},
|
|
||||||
journal = {Comm. ACM},
|
|
||||||
year = {1979},
|
|
||||||
volume = {22},
|
|
||||||
number = {11},
|
|
||||||
month = {November},
|
|
||||||
pages = {606--611}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{yd85,
|
|
||||||
author = {W. P. Yang and M. W. Du},
|
|
||||||
title = {A backtracking method for constructing perfect hash functions from a set of mapping functions},
|
|
||||||
journal = {BIT},
|
|
||||||
year = {1985},
|
|
||||||
volume = {25},
|
|
||||||
number = {1},
|
|
||||||
pages = {148--164}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{s85,
|
|
||||||
author = {T. J. Sager},
|
|
||||||
title = {A polynomial time generator for minimal perfect hash functions},
|
|
||||||
journal = {Commun. ACM},
|
|
||||||
year = {1985},
|
|
||||||
volume = {28},
|
|
||||||
number = {5},
|
|
||||||
month = {May},
|
|
||||||
pages = {523--532}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{cm93,
|
|
||||||
author = {Z. J. Czech and B. S. Majewski},
|
|
||||||
title = {A linear time algorithm for finding minimal perfect hash functions},
|
|
||||||
journal = {The computer Journal},
|
|
||||||
year = {1993},
|
|
||||||
volume = {36},
|
|
||||||
number = {6},
|
|
||||||
pages = {579--587}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{gbs94,
|
|
||||||
author = {R. Gupta and S. Bhaskar and S. Smolka},
|
|
||||||
title = {On randomization in sequential and distributed algorithms},
|
|
||||||
journal = {ACM Comput. Surveys},
|
|
||||||
year = {1994},
|
|
||||||
volume = {26},
|
|
||||||
number = {1},
|
|
||||||
month = {March},
|
|
||||||
pages = {7--86}
|
|
||||||
}
|
|
||||||
|
|
||||||
@InProceedings{sb84,
|
|
||||||
author = {C. Slot and P. V. E. Boas},
|
|
||||||
title = {On tape versus core; an application of space efficient perfect hash functions to the
|
|
||||||
invariance of space},
|
|
||||||
booktitle = {Proc. 16th Ann. ACM Symp. on Theory of Computing -- STOC'84},
|
|
||||||
address = {Washington},
|
|
||||||
month = {May},
|
|
||||||
year = {1984},
|
|
||||||
pages = {391--400},
|
|
||||||
}
|
|
||||||
|
|
||||||
@InProceedings{wi90,
|
|
||||||
author = {V. G. Winters},
|
|
||||||
title = {Minimal perfect hashing for large sets of data},
|
|
||||||
booktitle = {Internat. Conf. on Computing and Information -- ICCI'90},
|
|
||||||
address = {Canada},
|
|
||||||
month = {May},
|
|
||||||
year = {1990},
|
|
||||||
pages = {275--284},
|
|
||||||
}
|
|
||||||
|
|
||||||
@InProceedings{lr85,
|
|
||||||
author = {P. Larson and M. V. Ramakrishna},
|
|
||||||
title = {External perfect hashing},
|
|
||||||
booktitle = {Proc. ACM SIGMOD Conf.},
|
|
||||||
address = {Austin TX},
|
|
||||||
month = {June},
|
|
||||||
year = {1985},
|
|
||||||
pages = {190--199},
|
|
||||||
}
|
|
||||||
|
|
||||||
@Book{m84,
|
|
||||||
author = {K. Mehlhorn},
|
|
||||||
editor = {W. Brauer and G. Rozenberg and A. Salomaa},
|
|
||||||
title = {Data Structures and Algorithms 1: Sorting and Searching},
|
|
||||||
publisher = {Springer-Verlag},
|
|
||||||
year = {1984},
|
|
||||||
}
|
|
||||||
|
|
||||||
@PhdThesis{c92,
|
|
||||||
author = {Q. F. Chen},
|
|
||||||
title = {An Object-Oriented Database System for Efficient Information Retrieval Appliations},
|
|
||||||
school = {Virginia Tech Dept. of Computer Science},
|
|
||||||
year = {1992},
|
|
||||||
month = {March}
|
|
||||||
}
|
|
||||||
|
|
||||||
@article {er59,
|
|
||||||
AUTHOR = {Erd{\H{o}}s, P. and R{\'e}nyi, A.},
|
|
||||||
TITLE = {On random graphs {I}},
|
|
||||||
JOURNAL = {Pub. Math. Debrecen},
|
|
||||||
VOLUME = {6},
|
|
||||||
YEAR = {1959},
|
|
||||||
PAGES = {290--297},
|
|
||||||
MRCLASS = {05.00},
|
|
||||||
MRNUMBER = {MR0120167 (22 \#10924)},
|
|
||||||
MRREVIEWER = {A. Dvoretzky},
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@article {erdos61,
|
|
||||||
AUTHOR = {Erd{\H{o}}s, P. and R{\'e}nyi, A.},
|
|
||||||
TITLE = {On the evolution of random graphs},
|
|
||||||
JOURNAL = {Bull. Inst. Internat. Statist.},
|
|
||||||
VOLUME = 38,
|
|
||||||
YEAR = 1961,
|
|
||||||
PAGES = {343--347},
|
|
||||||
MRCLASS = {05.40 (55.10)},
|
|
||||||
MRNUMBER = {MR0148055 (26 \#5564)},
|
|
||||||
}
|
|
||||||
|
|
||||||
@article {er60,
|
|
||||||
AUTHOR = {Erd{\H{o}}s, P. and R{\'e}nyi, A.},
|
|
||||||
TITLE = {On the evolution of random graphs},
|
|
||||||
JOURNAL = {Magyar Tud. Akad. Mat. Kutat\'o Int. K\"ozl.},
|
|
||||||
VOLUME = {5},
|
|
||||||
YEAR = {1960},
|
|
||||||
PAGES = {17--61},
|
|
||||||
MRCLASS = {05.40},
|
|
||||||
MRNUMBER = {MR0125031 (23 \#A2338)},
|
|
||||||
MRREVIEWER = {J. Riordan},
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{er60:_Old,
|
|
||||||
author = {P. Erd{\H{o}}s and A. R\'enyi},
|
|
||||||
title = {On the evolution of random graphs},
|
|
||||||
journal = {Publications of the Mathematical Institute of the Hungarian
|
|
||||||
Academy of Sciences},
|
|
||||||
year = {1960},
|
|
||||||
volume = {56},
|
|
||||||
pages = {17-61}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{er61,
|
|
||||||
author = {P. Erd{\H{o}}s and A. R\'enyi},
|
|
||||||
title = {On the strength of connectedness of a random graph},
|
|
||||||
journal = {Acta Mathematica Scientia Hungary},
|
|
||||||
year = {1961},
|
|
||||||
volume = {12},
|
|
||||||
pages = {261-267}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Article{bp04,
|
|
||||||
author = {B. Bollob\'as and O. Pikhurko},
|
|
||||||
title = {Integer Sets with Prescribed Pairwise Differences Being Distinct},
|
|
||||||
journal = {European Journal of Combinatorics},
|
|
||||||
OPTkey = {},
|
|
||||||
OPTvolume = {},
|
|
||||||
OPTnumber = {},
|
|
||||||
OPTpages = {},
|
|
||||||
OPTmonth = {},
|
|
||||||
note = {To Appear},
|
|
||||||
OPTannote = {}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{pw04,
|
|
||||||
author = {B. Pittel and N. C. Wormald},
|
|
||||||
title = {Counting connected graphs inside-out},
|
|
||||||
journal = {Journal of Combinatorial Theory},
|
|
||||||
OPTkey = {},
|
|
||||||
OPTvolume = {},
|
|
||||||
OPTnumber = {},
|
|
||||||
OPTpages = {},
|
|
||||||
OPTmonth = {},
|
|
||||||
note = {To Appear},
|
|
||||||
OPTannote = {}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
@Article{mr95,
|
|
||||||
author = {M. Molloy and B. Reed},
|
|
||||||
title = {A critical point for random graphs with a given degree sequence},
|
|
||||||
journal = {Random Structures and Algorithms},
|
|
||||||
year = {1995},
|
|
||||||
volume = {6},
|
|
||||||
pages = {161-179}
|
|
||||||
}
|
|
||||||
|
|
||||||
@TechReport{bmz04,
|
|
||||||
author = {F. C. Botelho and D. Menoti and N. Ziviani},
|
|
||||||
title = {A New algorithm for constructing minimal perfect hash functions},
|
|
||||||
institution = {Federal Univ. of Minas Gerais},
|
|
||||||
year = {2004},
|
|
||||||
OPTkey = {},
|
|
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OPTtype = {},
|
|
||||||
number = {TR004},
|
|
||||||
OPTaddress = {},
|
|
||||||
OPTmonth = {},
|
|
||||||
note = {(http://www.dcc.ufmg.br/\texttt{\~ }nivio/pub/technicalreports.html)},
|
|
||||||
OPTannote = {}
|
|
||||||
}
|
|
||||||
|
|
||||||
@Article{mr98,
|
|
||||||
author = {M. Molloy and B. Reed},
|
|
||||||
title = {The size of the giant component of a random graph with a given degree sequence},
|
|
||||||
journal = {Combinatorics, Probability and Computing},
|
|
||||||
year = {1998},
|
|
||||||
volume = {7},
|
|
||||||
pages = {295-305}
|
|
||||||
}
|
|
||||||
|
|
||||||
@misc{h98,
|
|
||||||
author = {D. Hawking},
|
|
||||||
title = {Overview of TREC-7 Very Large Collection Track (Draft for Notebook)},
|
|
||||||
url = {citeseer.ist.psu.edu/4991.html},
|
|
||||||
year = {1998}}
|
|
||||||
|
|
||||||
@book {jlr00,
|
|
||||||
AUTHOR = {Janson, S. and {\L}uczak, T. and Ruci{\'n}ski, A.},
|
|
||||||
TITLE = {Random graphs},
|
|
||||||
PUBLISHER = {Wiley-Inter.},
|
|
||||||
YEAR = 2000,
|
|
||||||
PAGES = {xii+333},
|
|
||||||
ISBN = {0-471-17541-2},
|
|
||||||
MRCLASS = {05C80 (60C05 82B41)},
|
|
||||||
MRNUMBER = {2001k:05180},
|
|
||||||
MRREVIEWER = {Mark R. Jerrum},
|
|
||||||
}
|
|
||||||
|
|
||||||
@incollection {jlr90,
|
|
||||||
AUTHOR = {Janson, Svante and {\L}uczak, Tomasz and Ruci{\'n}ski,
|
|
||||||
Andrzej},
|
|
||||||
TITLE = {An exponential bound for the probability of nonexistence of a
|
|
||||||
specified subgraph in a random graph},
|
|
||||||
BOOKTITLE = {Random graphs '87 (Pozna\'n, 1987)},
|
|
||||||
PAGES = {73--87},
|
|
||||||
PUBLISHER = {Wiley},
|
|
||||||
ADDRESS = {Chichester},
|
|
||||||
YEAR = 1990,
|
|
||||||
MRCLASS = {05C80 (60C05)},
|
|
||||||
MRNUMBER = {91m:05168},
|
|
||||||
MRREVIEWER = {J. Spencer},
|
|
||||||
}
|
|
||||||
|
|
||||||
@book {b01,
|
|
||||||
AUTHOR = {Bollob{\'a}s, B.},
|
|
||||||
TITLE = {Random graphs},
|
|
||||||
SERIES = {Cambridge Studies in Advanced Mathematics},
|
|
||||||
VOLUME = 73,
|
|
||||||
EDITION = {Second},
|
|
||||||
PUBLISHER = {Cambridge University Press},
|
|
||||||
ADDRESS = {Cambridge},
|
|
||||||
YEAR = 2001,
|
|
||||||
PAGES = {xviii+498},
|
|
||||||
ISBN = {0-521-80920-7; 0-521-79722-5},
|
|
||||||
MRCLASS = {05C80 (60C05)},
|
|
||||||
MRNUMBER = {MR1864966 (2002j:05132)},
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
@ -1,73 +0,0 @@
|
||||||
\section{Trabalhos Relacionados}
|
|
||||||
As FHPs e FHPMs receberam muita aten\c{c}\~ao da comunidade
|
|
||||||
cient\'{\i}fica nas d\'ecadas de 80 e 90. Em~\cite{chm97} \'e
|
|
||||||
apresentado um survey completo da \'area at\'e 1997.
|
|
||||||
Nesta se\c{c}\~ao revisitamos os trabalhos cobertos pelo survey que
|
|
||||||
est\~ao diretamente relacionados aos algoritmos aqui propostos e
|
|
||||||
fazemos um survey dos algoritmos propostos desde ent\~ao.
|
|
||||||
|
|
||||||
Fredman, Koml\'os e Szemer\'edi~\cite{FKS84} mostraram que \'e poss\'{\i}vel construir
|
|
||||||
FHPs que podem ser descritas eficientemente em termos de espa\c{c}o e avaliadas em
|
|
||||||
tempo constante utilizando tamanhos de tabelas que s\~ao lineares no n\'umero de chaves:
|
|
||||||
$m=O(n)$.
|
|
||||||
No modelo de computa\c{c}\~ao deles, um elemento do universo~$U$ \'e colocado em uma
|
|
||||||
palavra de m\'aquina, e opera\c{c}\~oes aritm\'eticas e acesso \`a mem\'oria tem custo
|
|
||||||
$O(1)$.
|
|
||||||
Algoritmos rand\^omicos no modelo FKS podem construir FHPs com complexidade de tempo
|
|
||||||
experada de $O(n)$:
|
|
||||||
Este \'e o caso dos nossos algoritmos e dos trabalhos em~\cite{chm92,p99}.
|
|
||||||
|
|
||||||
Os trabalhos~\cite{asw00,swz00} apresentam algoritmos para construir
|
|
||||||
FHPs e FHPMs deterministicamente.
|
|
||||||
As fun\c{c}\~oes geradas necessitam de $O(n \log(n) + \log(\log(u)))$ bits para serem descritas.
|
|
||||||
A complexidade de caso m\'edio dos algoritmos para gerar as fun\c{c}\~oes \'e
|
|
||||||
$O(n\log(n) \log( \log (u)))$ e a de pior caso \'e $O(n^3\log(n) \log(\log(u)))$.
|
|
||||||
A complexidade de avalia\c{c}\~ao das fun\c{c}\~oes \'e $O(\log(n) + \log(\log(u)))$.
|
|
||||||
Assim, os algoritmos n\~ao geram fun\c{c}\~oes que podem ser avaliadas com complexidade
|
|
||||||
de tempo $O(1)$, est\~ao distantes a um fator de $\log n$ da complexidade \'otima para descrever
|
|
||||||
FHPs e FHPMs (Mehlhorn mostra em~\cite{m84}
|
|
||||||
que para armazenar uma FHP s\~ao necess\'arios no m\'{\i}nimo
|
|
||||||
$\Omega(n^2/(2\ln 2) m + \log\log u)$ bits), e n\~ao geram as
|
|
||||||
fun\c{c}\~oes com complexidade linear.
|
|
||||||
Al\'em disso, o universo $U$ das chaves \'e restrito a n\'umeros inteiros, o que pode
|
|
||||||
limitar a utiliza\c{c}\~ao na pr\'atica.
|
|
||||||
|
|
||||||
Pagh~\cite{p99} prop\^os uma fam\'{\i}lia de algoritmos rand\^omicos para construir
|
|
||||||
FHPMs.
|
|
||||||
A forma da fun\c{c}\~ao resultante \'e $h(k) = (f(k) + d_{g(k)}) \bmod n$,
|
|
||||||
onde $f$ e $g$ s\~ao fun\c{c}\~oes hash universal \cite{ss89} e $d$ \'e um conjunto de
|
|
||||||
valores de deslocamento para resolver as colis\~oes que s\~ao causadas pela fun\c{c}\~ao $f$.
|
|
||||||
Pagh identificou um conjunto de condi\c{c}\~oes referentes a $f$ e $g$, e mostrou
|
|
||||||
que se tais condi\c{c}\~oes fossem satisfeitas, ent\~ao, uma FHPM pode ser computada
|
|
||||||
em tempo esperado $O(n)$ e armazenada em $(2+\epsilon)n$ palavras de computador
|
|
||||||
(ou $O((2+\epsilon)n \log n)$ bits.)
|
|
||||||
Dietzfelbinger e Hagerup~\cite{dh01} melhoraram ~\cite{p99},
|
|
||||||
reduzindo de $(2+\epsilon)n$ para $(1+\epsilon)n$ (ou $O((1+\epsilon)n \log n)$ bits)
|
|
||||||
o n\'umero de palavras de
|
|
||||||
computador exigidas para armazenar a fun\c{c}\~ao, mas na abordagem deles $f$ e $g$
|
|
||||||
devem ser escolhidas de uma classe de fun\c{c}\~oes hash que atendam a requisitos
|
|
||||||
adicionais.
|
|
||||||
|
|
||||||
Galli, Seybold e Simon~\cite{gss01} propuseram um algoritmo r\^andomico
|
|
||||||
que gera FHPMs da mesma forma das geradas pelos algoritmos de Pagh~\cite{p99}
|
|
||||||
e, Dietzfelbinger e Hagerup~\cite{dh01}. No entanto, eles definiram a forma das
|
|
||||||
fun\c{c}\~oes $f(k) = h_c(k) \bmod n$ e $g(k) = \lfloor h_c(k)/n \rfloor$ para obter em tempo esperado $O(n)$ uma fun\c{c}\~ao que pode ser descrita em $O(n\log n)$ bits, onde
|
|
||||||
$h_c(k) = (ck \bmod p) \bmod n^2$, $1 \leq c \leq p-1$ e $p$ um primo maior do que $u$.
|
|
||||||
|
|
||||||
Os algoritmos propostos em~\cite{p99,dh01,gss01} n\~ao s\~ao escal\'aveis com o crescimento do
|
|
||||||
conjunto de chaves $S$. Isto \'e devido as restri\c{c}\~oes impostas sobre as fun\c{c}\~oes
|
|
||||||
hash universal utilizadas no c\'alculo das FHPMs. Normalmente \'e exigido um
|
|
||||||
n\'umero primo maior do que o tamanho do universo $u$ que, em geral, \'e muito maior
|
|
||||||
do que $n=|S|$ ou opera\c{c}\~oes envolvendo $n^2$ aparecem no c\'alculo da FHPM.
|
|
||||||
Al\'em disso, todas as fun\c{c}\~oes est\~ao distantes a um fator de $\log n$ da complexidade
|
|
||||||
\'otima para descrever FHPMs.
|
|
||||||
|
|
||||||
Diferentemente dos trabalhos em~\cite{p99,dh01,gss01}, nossos algoritmos usam
|
|
||||||
fun\c{c}\~oes hash universal que s\~ao selecionadas randomicamente de uma classe
|
|
||||||
de fun\c{c}\~oes que n\~ao necessitam atender restri\c{c}\~oes adicionais.
|
|
||||||
Al\'em disso, as FHPMs s\~ao geradas em tempo esperado $O(n)$, s\~ao avaliadas
|
|
||||||
com custo $O(1)$ e s\~ao descritas em $O(n)$ bits que est\'a muito pr\'oximo da
|
|
||||||
complexidade \'otima.
|
|
||||||
Pelo melhor do nosso conhecimento, os algoritmos propostos neste artigo s\~ao
|
|
||||||
os primeiros da literatura capazes de gerar FHPMs para conjuntos de chaves na
|
|
||||||
ordem de bilh\~oes de chaves utilizando um simples PC com 1GB de mem\'oria principal.
|
|
||||||
|
|
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% SVJour2 DOCUMENT CLASS OPTION SVGLOV2 -- for standardised journals
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style option for standardised journals]
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\itemsep0\p@}%
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%
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%ALT% \def\runheadhook{\rlap{\smash{\lower5pt\hbox to\textwidth{\hrulefill}}}}
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\if@twocolumn
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\AtEndOfClass{\setlength\columnsep{4mm}}
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\else
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\fi
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%
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\AtBeginDocument{%
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\@ifundefined{@journalname}
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<name of your journal>\string} in preambel^^J}}{}}
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%
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\endinput
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%%
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%% End of file `svglov2.clo'.
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||||||
%%%%%%%%%%%%%%%%%%%%%%% file template.tex %%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% This is a template file for the LaTeX package SVJour2 for the
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|
||||||
% Springer journal "The VLDB Journal".
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|
||||||
%
|
|
||||||
% Springer Heidelberg 2004/12/03
|
|
||||||
%
|
|
||||||
% Copy it to a new file with a new name and use it as the basis
|
|
||||||
% for your article. Delete % as needed.
|
|
||||||
%
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
||||||
%
|
|
||||||
% First comes an example EPS file -- just ignore it and
|
|
||||||
% proceed on the \documentclass line
|
|
||||||
% your LaTeX will extract the file if required
|
|
||||||
%\begin{filecontents*}{figs/minimalperfecthash-ph-mph.ps}
|
|
||||||
%!PS-Adobe-3.0 EPSF-3.0
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|
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%%BoundingBox: 19 19 221 221
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%%CreationDate: Mon Sep 29 1997
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|
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%%Creator: programmed by hand (JK)
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%%EndComments
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%gsave
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%newpath
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% 20 20 moveto
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%closepath
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%2 setlinewidth
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%gsave
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% .4 setgray fill
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%grestore
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||||||
%stroke
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|
||||||
%grestore
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|
||||||
%\end{filecontents*}
|
|
||||||
%
|
|
||||||
\documentclass[twocolumn,fleqn,runningheads]{svjour2}
|
|
||||||
%
|
|
||||||
\smartqed % flush right qed marks, e.g. at end of proof
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|
||||||
%
|
|
||||||
\usepackage{graphicx}
|
|
||||||
\usepackage{listings}
|
|
||||||
%
|
|
||||||
% \usepackage{mathptmx} % use Times fonts if available on your TeX system
|
|
||||||
%
|
|
||||||
% insert here the call for the packages your document requires
|
|
||||||
%\usepackage{latexsym}
|
|
||||||
% etc.
|
|
||||||
%
|
|
||||||
% please place your own definitions here and don't use \def but
|
|
||||||
% \newcommand{}{}
|
|
||||||
%
|
|
||||||
|
|
||||||
\lstset{
|
|
||||||
language=Pascal,
|
|
||||||
basicstyle=\fontsize{9}{9}\selectfont,
|
|
||||||
captionpos=t,
|
|
||||||
aboveskip=1mm,
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|
||||||
belowskip=1mm,
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|
||||||
abovecaptionskip=1mm,
|
|
||||||
belowcaptionskip=1mm,
|
|
||||||
% numbers = left,
|
|
||||||
mathescape=true,
|
|
||||||
escapechar=@,
|
|
||||||
extendedchars=true,
|
|
||||||
showstringspaces=false,
|
|
||||||
columns=fixed,
|
|
||||||
basewidth=0.515em,
|
|
||||||
frame=single,
|
|
||||||
framesep=2mm,
|
|
||||||
xleftmargin=2mm,
|
|
||||||
xrightmargin=2mm,
|
|
||||||
framerule=0.5pt
|
|
||||||
}
|
|
||||||
|
|
||||||
\def\cG{{\mathcal G}}
|
|
||||||
\def\crit{{\rm crit}}
|
|
||||||
\def\ncrit{{\rm ncrit}}
|
|
||||||
\def\scrit{{\rm scrit}}
|
|
||||||
\def\bedges{{\rm bedges}}
|
|
||||||
\def\ZZ{{\mathbb Z}}
|
|
||||||
|
|
||||||
\journalname{The VLDB Journal}
|
|
||||||
%
|
|
||||||
\begin{document}
|
|
||||||
|
|
||||||
\title{Minimal Perfect Hash Functions: New Algorithms and Applications\thanks{
|
|
||||||
This work was supported in part by
|
|
||||||
GERINDO Project--grant MCT/CNPq/CT-INFO 552.087/02-5,
|
|
||||||
CAPES/PROF Scholarship (Fabiano C. Botelho),
|
|
||||||
FAPESP Proj.\ Tem.\ 03/09925-5 and CNPq Grant 30.0334/93-1
|
|
||||||
(Yoshiharu Kohayakawa),
|
|
||||||
and CNPq Grant 30.5237/02-0 (Nivio Ziviani).}
|
|
||||||
}
|
|
||||||
%\subtitle{Do you have a subtitle?\\ If so, write it here}
|
|
||||||
|
|
||||||
%\titlerunning{Short form of title} % if too long for running head
|
|
||||||
|
|
||||||
\author{Fabiano C. Botelho \and Davi C. Reis \and Yoshiharu Kohayakawa \and Nivio Ziviani}
|
|
||||||
%\authorrunning{Short form of author list} % if too long for running head
|
|
||||||
\institute{
|
|
||||||
F. C. Botelho \and
|
|
||||||
N. Ziviani \at
|
|
||||||
Dept. of Computer Science,
|
|
||||||
Federal Univ. of Minas Gerais,
|
|
||||||
Belo Horizonte, Brazil\\
|
|
||||||
\email{\{fbotelho,nivio\}@dcc.ufmg.br}
|
|
||||||
\and
|
|
||||||
D. C. Reis \at
|
|
||||||
Google, Brazil \\
|
|
||||||
\email{davi.reis@gmail.com}
|
|
||||||
\and
|
|
||||||
Y. Kohayakawa
|
|
||||||
Dept. of Computer Science,
|
|
||||||
Univ. of S\~ao Paulo,
|
|
||||||
S\~ao Paulo, Brazil\\
|
|
||||||
\email{yoshi@ime.usp.br}
|
|
||||||
}
|
|
||||||
|
|
||||||
\date{Received: date / Accepted: date}
|
|
||||||
% The correct dates will be entered by the editor
|
|
||||||
|
|
||||||
|
|
||||||
\maketitle
|
|
||||||
|
|
||||||
\begin{abstract}
|
|
||||||
Insert your abstract here. Include up to five keywords.
|
|
||||||
\keywords{First keyword \and Second keyword \and More}
|
|
||||||
\end{abstract}
|
|
||||||
|
|
||||||
% main text
|
|
||||||
\input{introduction}
|
|
||||||
\input{relatedwork}
|
|
||||||
\input{algorithms}
|
|
||||||
\input{experimentalresults}
|
|
||||||
\input{applications}
|
|
||||||
\input{conclusions}
|
|
||||||
|
|
||||||
|
|
||||||
%\begin{acknowledgements}
|
|
||||||
%If you'd like to thank anyone, place your comments here
|
|
||||||
%and remove the percent signs.
|
|
||||||
%\end{acknowledgements}
|
|
||||||
|
|
||||||
% BibTeX users please use
|
|
||||||
%\bibliographystyle{spmpsci}
|
|
||||||
%\bibliography{} % name your BibTeX data base
|
|
||||||
\bibliographystyle{plain}
|
|
||||||
\bibliography{references}
|
|
||||||
\end{document}
|
|
||||||
Loading…
Reference in New Issue