From ab356bf19ba1ae272da2a756c1ed3d96d45fb56b Mon Sep 17 00:00:00 2001 From: fc_botelho Date: Tue, 27 Sep 2005 15:11:25 +0000 Subject: [PATCH] added vldb jounal --- vldb/ingles/algorithms.tex | 596 +++++++ vldb/ingles/applications.tex | 2 + vldb/ingles/conclusions.tex | 5 + vldb/ingles/experimentalresults.tex | 178 +++ vldb/ingles/figs/brz.fig | 135 ++ vldb/ingles/figs/brz.ps | 324 ++++ vldb/ingles/figs/grafordering.fig | 206 +++ vldb/ingles/figs/grafordering2.fig | 219 +++ vldb/ingles/figs/grafordering3.fig | 130 ++ vldb/ingles/figs/grafsearching.fig | 168 ++ vldb/ingles/figs/grafsearching2.fig | 180 +++ vldb/ingles/figs/grafsearchingncv.fig | 124 ++ .../ingles/figs/minimalperfecthash-ph-mph.fig | 176 ++ vldb/ingles/figs/minimalperfecthash-ph-mph.ps | 488 ++++++ vldb/ingles/introduction.tex | 86 + vldb/ingles/makefile | 17 + vldb/ingles/references.bib | 669 ++++++++ vldb/ingles/relatedwork.tex | 67 + vldb/ingles/svglov2.clo | 77 + vldb/ingles/svjour2.cls | 1419 +++++++++++++++++ vldb/ingles/vldb.tex | 150 ++ vldb/pt/algorithms.tex | 19 + vldb/pt/applications.tex | 2 + vldb/pt/conclusions.tex | 3 + vldb/pt/experimentalresults.tex | 1 + vldb/pt/figs/brz.fig | 135 ++ vldb/pt/figs/brz.ps | 324 ++++ vldb/pt/figs/grafordering.fig | 206 +++ vldb/pt/figs/grafordering2.fig | 219 +++ vldb/pt/figs/grafordering3.fig | 130 ++ vldb/pt/figs/grafsearching.fig | 168 ++ vldb/pt/figs/grafsearching2.fig | 180 +++ vldb/pt/figs/grafsearchingncv.fig | 124 ++ vldb/pt/figs/minimalperfecthash-ph-mph.fig | 176 ++ vldb/pt/figs/minimalperfecthash-ph-mph.ps | 488 ++++++ vldb/pt/introduction.tex | 13 + vldb/pt/makefile | 17 + vldb/pt/references.bib | 669 ++++++++ vldb/pt/relatedwork.tex | 2 + vldb/pt/svglov2.clo | 77 + vldb/pt/svjour2.cls | 1419 +++++++++++++++++ vldb/pt/vldb.tex | 150 ++ 42 files changed, 9938 insertions(+) create mode 100755 vldb/ingles/algorithms.tex create mode 100644 vldb/ingles/applications.tex create mode 100755 vldb/ingles/conclusions.tex create mode 100755 vldb/ingles/experimentalresults.tex create mode 100644 vldb/ingles/figs/brz.fig create mode 100644 vldb/ingles/figs/brz.ps create mode 100755 vldb/ingles/figs/grafordering.fig create mode 100755 vldb/ingles/figs/grafordering2.fig create mode 100755 vldb/ingles/figs/grafordering3.fig create mode 100755 vldb/ingles/figs/grafsearching.fig create mode 100755 vldb/ingles/figs/grafsearching2.fig create mode 100755 vldb/ingles/figs/grafsearchingncv.fig create mode 100755 vldb/ingles/figs/minimalperfecthash-ph-mph.fig create mode 100755 vldb/ingles/figs/minimalperfecthash-ph-mph.ps create mode 100755 vldb/ingles/introduction.tex create mode 100755 vldb/ingles/makefile create mode 100755 vldb/ingles/references.bib create mode 100755 vldb/ingles/relatedwork.tex create mode 100644 vldb/ingles/svglov2.clo create mode 100644 vldb/ingles/svjour2.cls create mode 100644 vldb/ingles/vldb.tex create mode 100755 vldb/pt/algorithms.tex create mode 100644 vldb/pt/applications.tex create mode 100755 vldb/pt/conclusions.tex create mode 100755 vldb/pt/experimentalresults.tex create mode 100644 vldb/pt/figs/brz.fig create mode 100644 vldb/pt/figs/brz.ps create mode 100755 vldb/pt/figs/grafordering.fig create mode 100755 vldb/pt/figs/grafordering2.fig create mode 100755 vldb/pt/figs/grafordering3.fig create mode 100755 vldb/pt/figs/grafsearching.fig create mode 100755 vldb/pt/figs/grafsearching2.fig create mode 100755 vldb/pt/figs/grafsearchingncv.fig create mode 100755 vldb/pt/figs/minimalperfecthash-ph-mph.fig create mode 100755 vldb/pt/figs/minimalperfecthash-ph-mph.ps create mode 100755 vldb/pt/introduction.tex create mode 100755 vldb/pt/makefile create mode 100755 vldb/pt/references.bib create mode 100755 vldb/pt/relatedwork.tex create mode 100644 vldb/pt/svglov2.clo create mode 100644 vldb/pt/svjour2.cls create mode 100644 vldb/pt/vldb.tex diff --git a/vldb/ingles/algorithms.tex b/vldb/ingles/algorithms.tex new file mode 100755 index 0000000..226fbe5 --- /dev/null +++ b/vldb/ingles/algorithms.tex @@ -0,0 +1,596 @@ +\section{The Algorithms} +\label{sec:thealgorithm} +We are going to present a novel algorithm that extends our previous work +presented in~\cite{bkz05}. +First we describe our previous work and in the following the new algorithm. +To the best of our knowledge this work is the first one that becomes possible +the construction of minimal perfect hash functions for sets in the order of +billion of keys efficiently. +And better, the generated functions are very compact and can be represented +using approximately nine bits per key. + +\subsection{A Main Memory Based Algorithm} + +\subsection{An External Memory Based Algorithm} +The idea of behind the new algorithm is the traditional divide-to-conquer approach. +The new algorithm consists of two steps that are presented in Fig.~\ref{fig:new-algo-main-steps}: +\begin{enumerate} +\item Using an universal hashing function~\cite{ss89} $h_1: S \to B$ the keys from $S$ are segmented to +a bucket set B, where $|B| = b$. We choice parameter $b$ in such way that any bucket will +contain more than 256 keys. +This choice is crucial to make the new algorithm works and we give details about it hereinafter. +\item The keys in each bucket are separetaly spread into a hash table. +\end{enumerate} +% 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} + +The main novelties are in the way the keys are segmented using external memory and spread using +minimal perfect hash functions for each bucket. The next two sections describe each step in details. +\subsubsection{Segmentation} +\subsubsection{Spreading} +% Let us show how the minimal perfect hash function~$h$ +% will be constructed. +% We make use of three auxiliary random functions~$h_1$, $h_2$ and~$h_3:U\to V$, +% where~$V=[0,t-1]$ for some suitably chosen integer~$t=cn$, where +% $n=|S|$. +% We build a random graph~$G=G(h_1,h_2)$ on~$V$, +% whose edge set is~$\big\{\{h_1(x),h_2(x)\}:x\in S\big\}$. +% There is an edge in~$G$ for each key in the set of keys~$S$. +% +% In what follows, we shall be interested in the \textit{2-core} of +% the random graph~$G$, that is, the maximal subgraph of~$G$ with minimal +% degree at least~$2$ +% (see, e.g., \cite{b01,jlr00}). +% Because of its importance in our context, we call the 2-core the +% \textit{critical} subgraph of~$G$ and denote it by~$G_\crit$. +% The vertices and edges in~$G_\crit$ are said to be \textit{critical}. +% We let~$V_\crit=V(G_\crit)$ and~$E_\crit=E(G_\crit)$. +% Moreover, we let~$V_\ncrit=V-V_\crit$ be the set of {\em non-critical} +% vertices in~$G$. +% We also let~$V_\scrit\subseteq V_\crit$ be the set of all critical +% vertices that have at least one non-critical vertex as a neighbour. +% Let $E_\ncrit=E(G)-E_\crit$ be the set of {\em non-critical} edges in~$G$. +% Finally, we let~$G_\ncrit=(V_\ncrit\cup V_\scrit,E_\ncrit)$ be the +% {\em non-critical} subgraph of~$G$. +% The non-critical subgraph $G_\ncrit$ corresponds to the ``acyclic part'' +% of~$G$. +% We have $G=G_\crit\cup G_\ncrit$. +% +% We then construct a suitable labelling $g:V\to\ZZ$ of the vertices +% of~$G$: we choose~$g(v)$ for each~$v\in V(G)$ in such +% a way that~$h(x)=g(h_1(x))+g(h_2(x))$ ($x\in S$) is a +% minimal perfect hash function for~$S$. +% We will see later on that this labelling~$g$ can be found in linear time +% if the number of edges in $G_\crit$ is at most $\frac{1}{2}|E(G)|$. +% +% Figure~\ref{prog:mainsteps} presents a pseudo code for the algorithm. +% The procedure GenerateMPHF ($S$, $g$) receives as input the set of +% keys~$S$ and produces the labelling~$g$. +% The method uses a mapping, ordering and searching approach. +% We now describe each step. +% +% \enlargethispage{\baselineskip} +% \enlargethispage{\baselineskip} +% \vspace{-11pt} +% \begin{figure}[htb] +% \begin{center} +% \begin{lstlisting}[ +% ] +% procedure @GenerateMPHF@ (@$S$@, @$g$@) +% Mapping (@$S$@, @$G$@); +% Ordering (@$G$@, @$G_\crit$@, @$G_\ncrit$@); +% Searching (@$G$@, @$G_\crit$@, @$G_\ncrit$@, @$g$@); +% \end{lstlisting} +% \end{center} +% \vspace{-12pt} +% \caption{Main steps of the algorithm for constructing a minimal +% perfect hash function} +% \vspace{-26pt} +% \label{prog:mainsteps} +% \end{figure} +% +% \subsection{Mapping Step} +% \label{sec:mapping} +% +% The procedure Mapping ($S$, $G$) receives as input the set of keys~$S$ and +% generates the random graph $G=G(h_1,h_2)$, by generating two auxiliary +% functions~$h_1$, $h_2:U\to[0,t-1]$. +% +% \def\tabela{\hbox{table}} +% % +% The functions~$h_1$ and~$h_2$ are constructed as follows. +% We impose some upper bound~$L$ on the lengths of the keys in~$S$. +% To define~$h_j$ ($j=1$,$2$), we generate an~$L\times\Sigma$ table +% of random integers~$\tabela_j$. +% For a key~$x\in S$ of length~$|x|\leq L$ and~$j\in\{1,2\}$, we let +% \begin{displaymath} \nonumber +% h_j(x) = \Big (\textstyle\sum_{i=1}^{|x|} \tabela_j[i, x[i]] \Big) \bmod t. +% \end{displaymath} +% The random graph~$G=G(h_1,h_2)$ has vertex set~$V=[0,t-1]$ and edge set +% $\big\{\{h_1(x),h_2(x)\}:x\in S\big\}$. We need~$G$ to be +% simple, i.e., +% $G$~should have neither loops nor multiple edges. +% A loop occurs when $h_1(x) = h_2(x)$ for some~$x\in S$. +% We solve this in an ad hoc manner: we simply let~$h_2(x)=(2h_1(x)+1)\bmod +% t$ in this case. +% If we still find a loop after this, +% we generate another pair $(h_1,h_2)$. +% When a multiple edge occurs we abort and generate a new pair~$(h_1,h_2)$. +% +% \vspace{-10pt} +% \subsubsection{Analysis of the Mapping Step. } +% +% We start by discussing some facts on random graphs. +% Let~$G=(V,E)$ with $|V|=t$ and $|E|=n$ be a random graph in the uniform +% model~$\cG(t,n)$, the model in which all the~${{t\choose2}\choose n}$ graphs +% on~$V$ with~$n$ edges are equiprobable. +% The study of~$\cG(t,n)$ goes back to the classical +% work of Erd\H os and R\'enyi~\cite{er59,er60,er61} (for a modern treatment, +% see~\cite{b01,jlr00}). +% Let $d=2n/t$ be the average degree of $G$. +% It is well known that, if~$d>1$, or, equivalently, +% if~$c<2$ (recall that we have $t=cn$), +% then, almost every~$G$ +% contains\footnote{As is usual in the theory of random graphs, we use +% the terms `almost every' and `almost surely' to mean `with probability +% tending to~$1$ as~$t\to\infty$'.} a ``giant'' component of +% order~$(1+o(1))bt$, where~$b=1-T/d$, and~$00$ +% as~$n\to\infty$, the expected number of iterations is~$e^{1/c^2}=2.13$ (recall +% $c=1.15$). +% As the expected number of iterations is $O(1)$, the mapping step takes +% $O(n)$ time. +% +% \vspace{-5pt} +% \subsection{Ordering Step} +% \label{sec:ordering} +% +% The procedure Ordering ($G$, $G_\crit$, $G_\ncrit$) receives as +% input the graph~$G$ and partitions~$G$ into the two subgraphs +% $G_\crit$ and $G_\ncrit$, so that~$G=G_\crit\cup G_\ncrit$. +% For that, the procedure iteratively remove all vertices of degree 1 until done. +% +% \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} diff --git a/vldb/ingles/applications.tex b/vldb/ingles/applications.tex new file mode 100644 index 0000000..cd6e72b --- /dev/null +++ b/vldb/ingles/applications.tex @@ -0,0 +1,2 @@ +\section{Applications} +\label{sec:applications} \ No newline at end of file diff --git a/vldb/ingles/conclusions.tex b/vldb/ingles/conclusions.tex new file mode 100755 index 0000000..a71789c --- /dev/null +++ b/vldb/ingles/conclusions.tex @@ -0,0 +1,5 @@ +\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. diff --git a/vldb/ingles/experimentalresults.tex b/vldb/ingles/experimentalresults.tex new file mode 100755 index 0000000..3193625 --- /dev/null +++ b/vldb/ingles/experimentalresults.tex @@ -0,0 +1,178 @@ +\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. 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/dev/null +++ b/vldb/ingles/introduction.tex @@ -0,0 +1,86 @@ +\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. diff --git a/vldb/ingles/makefile b/vldb/ingles/makefile new file mode 100755 index 0000000..c1a738f --- /dev/null +++ b/vldb/ingles/makefile @@ -0,0 +1,17 @@ +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 + diff --git a/vldb/ingles/references.bib b/vldb/ingles/references.bib new file mode 100755 index 0000000..6f54cbe --- /dev/null +++ b/vldb/ingles/references.bib @@ -0,0 +1,669 @@ +@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} +} + +@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�os para a Constru�o de Arquivos invertidos}, + school = {Departamento de Ci�cia da Computa�o, Universidade Federal de Minas Gerais}, + year = 2000, + month = {Mar�}, + 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. 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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. 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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. 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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 = {}, + 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)}, +} + diff --git a/vldb/ingles/relatedwork.tex b/vldb/ingles/relatedwork.tex new file mode 100755 index 0000000..e32c52e --- /dev/null +++ b/vldb/ingles/relatedwork.tex @@ -0,0 +1,67 @@ +\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~$1/p \simeq 2.92$. \ No newline at end of file diff --git a/vldb/ingles/svglov2.clo b/vldb/ingles/svglov2.clo new file mode 100644 index 0000000..d98306e --- /dev/null +++ b/vldb/ingles/svglov2.clo @@ -0,0 +1,77 @@ +% 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 \! 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Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% 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{% +\string} in preambel^^J}}{}} +% +\endinput +%% +%% End of file `svglov2.clo'. diff --git a/vldb/ingles/svjour2.cls b/vldb/ingles/svjour2.cls new file mode 100644 index 0000000..56d9216 --- /dev/null +++ b/vldb/ingles/svjour2.cls @@ -0,0 +1,1419 @@ +% SVJour2 DOCUMENT CLASS -- version 2.8 for LaTeX2e +% +% LaTeX 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 \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{svjour2}[2005/08/29 v2.8 +^^JLaTeX document class for Springer journals] +\newcommand\@ptsize{} +\newif\if@restonecol +\newif\if@titlepage +\@titlepagefalse +\DeclareOption{a4paper} + {\setlength\paperheight {297mm}% + \setlength\paperwidth {210mm}} +\DeclareOption{10pt}{\renewcommand\@ptsize{0}} +\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue} +\DeclareOption{draft}{\setlength\overfullrule{5pt}} +\DeclareOption{final}{\setlength\overfullrule{0pt}} +\DeclareOption{fleqn}{\input{fleqn.clo}\AtBeginDocument{\mathindent\z@}} +\DeclareOption{twocolumn}{\@twocolumntrue\ExecuteOptions{fleqn}} +\newif\if@avier\@avierfalse +\DeclareOption{onecollarge}{\@aviertrue} +\let\if@mathematic\iftrue +\let\if@numbook\iffalse +\DeclareOption{numbook}{\let\if@envcntsect\iftrue + \AtEndOfPackage{% + \renewcommand\thefigure{\thesection.\@arabic\c@figure}% + \renewcommand\thetable{\thesection.\@arabic\c@table}% + \renewcommand\theequation{\thesection.\@arabic\c@equation}% + \@addtoreset{figure}{section}% + \@addtoreset{table}{section}% + \@addtoreset{equation}{section}% + }% +} +\DeclareOption{openbib}{% + \AtEndOfPackage{% + \renewcommand\@openbib@code{% + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + }% + \renewcommand\newblock{\par}}% +} +\DeclareOption{natbib}{% +\AtEndOfClass{\RequirePackage{natbib}% +% Changing some parameters of NATBIB +\setlength{\bibhang}{\parindent}% +%\setlength{\bibsep}{0mm}% +\let\bibfont=\small +\def\@biblabel#1{#1.}% +\newcommand{\etal}{et al.}% +\bibpunct{(}{)}{;}{a}{}{,}}} +% +\let\if@runhead\iffalse +\DeclareOption{runningheads}{\let\if@runhead\iftrue} +\let\if@smartrunh\iffalse +\DeclareOption{smartrunhead}{\let\if@smartrunh\iftrue} +\DeclareOption{nosmartrunhead}{\let\if@smartrunh\iffalse} +\let\if@envcntreset\iffalse +\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue} +\let\if@envcntsame\iffalse +\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue} +\let\if@envcntsect\iffalse +\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue} +\let\if@referee\iffalse +\DeclareOption{referee}{\let\if@referee\iftrue} +\def\makereferee{\def\baselinestretch{2}} +\let\if@instindent\iffalse +\DeclareOption{instindent}{\let\if@instindent\iftrue} +\let\if@smartand\iffalse +\DeclareOption{smartand}{\let\if@smartand\iftrue} +\let\if@spthms\iftrue +\DeclareOption{nospthms}{\let\if@spthms\iffalse} +% +% language and babel dependencies +\DeclareOption{deutsch}{\def\switcht@@therlang{\switcht@deutsch}% +\gdef\svlanginfo{\typeout{Man spricht deutsch.}\global\let\svlanginfo\relax}} +\DeclareOption{francais}{\def\switcht@@therlang{\switcht@francais}% +\gdef\svlanginfo{\typeout{On parle francais.}\global\let\svlanginfo\relax}} +\let\switcht@@therlang\relax +\let\svlanginfo\relax +% +\AtBeginDocument{\@ifpackageloaded{babel}{% +\@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}% +\@ifundefined{extrasUKenglish}{}{\addto\extrasUKenglish{\switcht@albion}}% +\@ifundefined{extrasfrenchb}{}{\addto\extrasfrenchb{\switcht@francais}}% +\@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}% +\@ifundefined{extrasngerman}{}{\addto\extrasngerman{\switcht@deutsch}}% +}{\switcht@@therlang}% +} +% +\def\ClassInfoNoLine#1#2{% + \ClassInfo{#1}{#2\@gobble}% +} +\let\journalopt\@empty +\DeclareOption*{% +\InputIfFileExists{sv\CurrentOption.clo}{% +\global\let\journalopt\CurrentOption}{% +\ClassWarning{Springer-SVJour2}{Specified option or subpackage +"\CurrentOption" not found -}\OptionNotUsed}} +\ExecuteOptions{a4paper,twoside,10pt,instindent} +\ProcessOptions +% +\ifx\journalopt\@empty\relax +\ClassInfoNoLine{Springer-SVJour2}{extra/valid Springer sub-package (-> *.clo) +\MessageBreak not found in option list of \string\documentclass +\MessageBreak - autoactivating "global" style}{} +\input{svglov2.clo} +\else +\@ifundefined{validfor}{% +\ClassError{Springer-SVJour2}{Possible option clash for sub-package +\MessageBreak "sv\journalopt.clo" - option file not valid +\MessageBreak for this class}{Perhaps you used an option of the old +Springer class SVJour!} +}{} +\fi +% +\if@smartrunh\AtEndDocument{\islastpageeven\getlastpagenumber}\fi +% +\newcommand{\twocoltest}[2]{\if@twocolumn\def\@gtempa{#2}\else\def\@gtempa{#1}\fi +\@gtempa\makeatother} +\newcommand{\columncase}{\makeatletter\twocoltest} +% +\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00} +\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01} +\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02} +\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03} +\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04} +\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05} +\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06} +\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07} +\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08} +\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09} +\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A} +% +\setlength\parindent{15\p@} +\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@} +\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@} +\setlength\headheight{12\p@} +\setlength\headsep {16.74dd} +\setlength\topskip {10\p@} +\setlength\footskip{30\p@} +\setlength\maxdepth{.5\topskip} +% +\@settopoint\textwidth +\setlength\marginparsep {10\p@} +\setlength\marginparpush{5\p@} +\setlength\topmargin{-10pt} +\if@twocolumn + \setlength\oddsidemargin {-30\p@} + \setlength\evensidemargin{-30\p@} +\else + \setlength\oddsidemargin {\z@} + \setlength\evensidemargin{\z@} +\fi +\setlength\marginparwidth {48\p@} +\setlength\footnotesep{8\p@} +\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@} +\setlength\floatsep {12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\textfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@} +\setlength\intextsep {20\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\dblfloatsep {12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@} +\setlength\@fptop{0\p@} +\setlength\@fpsep{12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\@fpbot{0\p@ \@plus 1fil} +\setlength\@dblfptop{0\p@} +\setlength\@dblfpsep{12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\@dblfpbot{0\p@ \@plus 1fil} +\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@} +\def\@listi{\leftmargin\leftmargini + \parsep \z@ + \topsep 6\p@ \@plus2\p@ \@minus4\p@ + \itemsep\parsep} +\let\@listI\@listi +\@listi +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep \z@ + \parsep \topsep + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep \z@ + \parsep \topsep + \itemsep \parsep} +\def\@listiv {\leftmargin\leftmarginiv + \labelwidth\leftmarginiv + \advance\labelwidth-\labelsep} +\def\@listv {\leftmargin\leftmarginv + \labelwidth\leftmarginv + \advance\labelwidth-\labelsep} +\def\@listvi {\leftmargin\leftmarginvi + \labelwidth\leftmarginvi + \advance\labelwidth-\labelsep} +% +\setlength\lineskip{1\p@} +\setlength\normallineskip{1\p@} +\renewcommand\baselinestretch{} +\setlength\parskip{0\p@ \@plus \p@} +\@lowpenalty 51 +\@medpenalty 151 +\@highpenalty 301 +\setcounter{topnumber}{4} +\renewcommand\topfraction{.9} +\setcounter{bottomnumber}{2} +\renewcommand\bottomfraction{.7} +\setcounter{totalnumber}{6} +\renewcommand\textfraction{.1} +\renewcommand\floatpagefraction{.85} +\setcounter{dbltopnumber}{3} +\renewcommand\dbltopfraction{.85} +\renewcommand\dblfloatpagefraction{.85} +\def\ps@headings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\small\csname runheadhook\endcsname + \rlap{\thepage}\hfil\leftmark\unskip}% + \def\@oddhead{\small\csname runheadhook\endcsname + \ignorespaces\rightmark\hfil\llap{\thepage}}% + \let\@mkboth\@gobbletwo + \let\sectionmark\@gobble + \let\subsectionmark\@gobble + } +% make indentations changeable +\def\setitemindent#1{\settowidth{\labelwidth}{#1}% + \leftmargini\labelwidth + \advance\leftmargini\labelsep + \def\@listi{\leftmargin\leftmargini + \labelwidth\leftmargini\advance\labelwidth by -\labelsep + \parsep=\parskip + \topsep=\medskipamount + \itemsep=\parskip \advance\itemsep by -\parsep}} +\def\setitemitemindent#1{\settowidth{\labelwidth}{#1}% + \leftmarginii\labelwidth + \advance\leftmarginii\labelsep +\def\@listii{\leftmargin\leftmarginii + \labelwidth\leftmarginii\advance\labelwidth by -\labelsep + \parsep=\parskip + \topsep=\z@ + \itemsep=\parskip \advance\itemsep by -\parsep}} +% labels of description +\def\descriptionlabel#1{\hspace\labelsep #1\hfil} +% adjusted environment "description" +% if an optional parameter (at the first two levels of lists) +% is present, its width is considered to be the widest mark +% throughout the current list. +\def\description{\@ifnextchar[{\@describe}{\list{}{\labelwidth\z@ + \itemindent-\leftmargin \let\makelabel\descriptionlabel}}} +\let\enddescription\endlist +% +\def\describelabel#1{#1\hfil} +\def\@describe[#1]{\relax\ifnum\@listdepth=0 +\setitemindent{#1}\else\ifnum\@listdepth=1 +\setitemitemindent{#1}\fi\fi +\list{--}{\let\makelabel\describelabel}} +% +\newdimen\logodepth +\logodepth=1.2cm +\newdimen\headerboxheight +\headerboxheight=180pt % 18 10.5dd-lines - 2\baselineskip +\advance\headerboxheight by-14.5mm +\newdimen\betweenumberspace % dimension for space between +\betweenumberspace=3.33pt % number and text of titles. +\newdimen\aftertext % dimension for space after +\aftertext=5pt % text of title. +\newdimen\headlineindent % dimension for space between +\headlineindent=1.166cm % number and text of headings. +\if@mathematic + \def\runinend{} % \enspace} + \def\floatcounterend{\enspace} + \def\sectcounterend{} +\else + \def\runinend{.} + \def\floatcounterend{.\ } + \def\sectcounterend{.} +\fi +\def\email#1{\emailname: #1} +\def\keywords#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\keywordname\enspace\ignorespaces#1\par}} +% +\def\subclassname{{\bfseries Mathematics Subject Classification +(2000)}\enspace} +\def\subclass#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\subclassname\ignorespaces#1\par}} +% +\def\PACSname{\textbf{PACS}\enspace} +\def\PACS#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\PACSname\ignorespaces#1\par}} +% +\def\CRclassname{{\bfseries CR Subject Classification}\enspace} +\def\CRclass#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\CRclassname\ignorespaces#1\par}} +% +\def\ESMname{\textbf{Electronic Supplementary Material}\enspace} +\def\ESM#1{\par\addvspace\medskipamount +\noindent\ESMname\ignorespaces#1\par} +% +\newcounter{inst} +\newcounter{auth} +\def\authdepth{2} +\newdimen\instindent +\newbox\authrun +\newtoks\authorrunning +\newbox\titrun +\newtoks\titlerunning +\def\authorfont{\bfseries} + +\def\combirunning#1{\gdef\@combi{#1}} +\def\@combi{} +\newbox\combirun +% +\def\ps@last{\def\@evenhead{\small\rlap{\thepage}\hfil +\lastevenhead}} +\newcounter{lastpage} +\def\islastpageeven{\@ifundefined{lastpagenumber} +{\setcounter{lastpage}{0}}{\setcounter{lastpage}{\lastpagenumber}} +\ifnum\value{lastpage}>0 + \ifodd\value{lastpage}% + \else + \if@smartrunh + \thispagestyle{last}% + \fi + \fi +\fi} +\def\getlastpagenumber{\clearpage +\addtocounter{page}{-1}% + \immediate\write\@auxout{\string\gdef\string\lastpagenumber{\thepage}}% + \immediate\write\@auxout{\string\newlabel{LastPage}{{}{\thepage}}}% + \addtocounter{page}{1}} + +\def\journalname#1{\gdef\@journalname{#1}} + +\def\dedication#1{\gdef\@dedic{#1}} +\def\@dedic{} + +\let\@date\undefined +\def\notused{~} + +\def\institute#1{\gdef\@institute{#1}} + +\def\offprints#1{\begingroup +\def\protect{\noexpand\protect\noexpand}\xdef\@thanks{\@thanks +\protect\footnotetext[0]{\unskip\hskip-15pt{\itshape Send offprint requests +to\/}: \ignorespaces#1}}\endgroup\ignorespaces} + +%\def\mail#1{\gdef\@mail{#1}} +%\def\@mail{} + +\def\@thanks{} + +\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}% + \or \dagger\or \ddagger\or + \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger + \or \ddagger\ddagger \else\@ctrerr\fi\relax} +% +%\def\invthanks#1{\footnotetext[0]{\kern-\bibindent#1}} +% +\def\nothanksmarks{\def\thanks##1{\protected@xdef\@thanks{\@thanks + \protect\footnotetext[0]{\kern-\bibindent##1}}}} +% +\def\subtitle#1{\gdef\@subtitle{#1}} +\def\@subtitle{} + +\def\headnote#1{\gdef\@headnote{#1}} +\def\@headnote{} + +\def\papertype#1{\gdef\paper@type{\MakeUppercase{#1}}} +\def\paper@type{} + +\def\ch@ckobl#1#2{\@ifundefined{@#1} + {\typeout{SVJour2 warning: Missing +\expandafter\string\csname#1\endcsname}% + \csname #1\endcsname{#2}} + {}} +% +\def\ProcessRunnHead{% + \def\\{\unskip\ \ignorespaces}% + \def\thanks##1{\unskip{}}% + \instindent=\textwidth + \advance\instindent by-\headlineindent + \if!\the\titlerunning!\else + \edef\@title{\the\titlerunning}% + \fi + \global\setbox\titrun=\hbox{\small\rmfamily\unboldmath\ignorespaces\@title + \unskip}% + \ifdim\wd\titrun>\instindent + \typeout{^^JSVJour2 Warning: Title too long for running head.}% + \typeout{Please supply a shorter form with \string\titlerunning + \space prior to \string\maketitle}% + \global\setbox\titrun=\hbox{\small\rmfamily + Title Suppressed Due to Excessive Length}% + \fi + \xdef\@title{\copy\titrun}% +% + \if!\the\authorrunning! + \else + \setcounter{auth}{1}% + \edef\@author{\the\authorrunning}% + \fi + \ifnum\value{inst}>\authdepth + \def\stripauthor##1\and##2\endauthor{% + \protected@xdef\@author{##1\unskip\unskip\if!##2!\else\ et al.\fi}}% + \expandafter\stripauthor\@author\and\endauthor + \else + \gdef\and{\unskip, \ignorespaces}% + {\def\and{\noexpand\protect\noexpand\and}% + \protected@xdef\@author{\@author}} + \fi + \global\setbox\authrun=\hbox{\small\rmfamily\unboldmath\ignorespaces + \@author\unskip}% + \ifdim\wd\authrun>\instindent + \typeout{^^JSVJour2 Warning: Author name(s) too long for running head. + ^^JPlease supply a shorter form with \string\authorrunning + \space prior to \string\maketitle}% + \global\setbox\authrun=\hbox{\small\rmfamily Please give a shorter version + with: {\tt\string\authorrunning\space and + \string\titlerunning\space prior to \string\maketitle}}% + \fi + \xdef\@author{\copy\authrun}% + \markboth{\@author}{\@title}% +} +% +\let\orithanks=\thanks +\def\thanks#1{\ClassWarning{SVJour2}{\string\thanks\space may only be +used inside of \string\title, \string\author,\MessageBreak +and \string\date\space prior to \string\maketitle}} +% +\def\maketitle{\par\let\thanks=\orithanks +\ch@ckobl{journalname}{Noname} +\ch@ckobl{date}{the date of receipt and acceptance should be inserted +later} +\ch@ckobl{title}{A title should be given} +\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given} +\ch@ckobl{institute}{Address(es) of author(s) should be given} +\begingroup +% + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \def\@makefnmark{$^{\@thefnmark}$}% + \renewcommand\@makefntext[1]{% + \noindent + \hb@xt@\bibindent{\hss\@makefnmark\enspace}##1\vrule height0pt + width0pt depth8pt} +% + \def\lastand{\ifnum\value{inst}=2\relax + \unskip{} \andname\ + \else + \unskip, \andname\ + \fi}% + \def\and{\stepcounter{auth}\relax + \if@smartand + \ifnum\value{auth}=\value{inst}% + \lastand + \else + \unskip, + \fi + \else + \unskip, + \fi}% + \thispagestyle{empty} + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi +% + \global\@topnum\z@ + \if!\@thanks!\else + \@thanks +\insert\footins{\vskip-3pt\hrule width\columnwidth\vskip3pt}% + \fi + {\def\thanks##1{\unskip{}}% + \def\iand{\\[5pt]\let\and=\nand}% + \def\nand{\ifhmode\unskip\nobreak\fi\ $\cdot$ }% + \let\and=\nand + \def\at{\\\let\and=\iand}% + \footnotetext[0]{\kern-\bibindent + \ignorespaces\@institute}\vspace{5dd}}% +%\if!\@mail!\else +% \footnotetext[0]{\kern-\bibindent\mailname\ +% \ignorespaces\@mail}% +%\fi +% + \if@runhead + \ProcessRunnHead + \fi +% + \endgroup + \setcounter{footnote}{0} + \global\let\thanks\relax + \global\let\maketitle\relax + \global\let\@maketitle\relax + \global\let\@thanks\@empty + \global\let\@author\@empty + \global\let\@date\@empty + \global\let\@title\@empty + \global\let\@subtitle\@empty + \global\let\title\relax + \global\let\author\relax + \global\let\date\relax + \global\let\and\relax} + +\def\makeheadbox{{% +\hbox to0pt{\vbox{\baselineskip=10dd\hrule\hbox +to\hsize{\vrule\kern3pt\vbox{\kern3pt +\hbox{\bfseries\@journalname\ manuscript No.} +\hbox{(will be inserted by the editor)} +\kern3pt}\hfil\kern3pt\vrule}\hrule}% +\hss}}} +% +\def\rubric{\setbox0=\hbox{\small\strut}\@tempdima=\ht0\advance +\@tempdima\dp0\advance\@tempdima2\fboxsep\vrule\@height\@tempdima +\@width\z@} +\newdimen\rubricwidth +% +\def\@maketitle{\newpage +\normalfont +\vbox to0pt{\if@twocolumn\vskip-39pt\else\vskip-49pt\fi +\nointerlineskip +\makeheadbox\vss}\nointerlineskip +\vbox to 0pt{\offinterlineskip\rubricwidth=\columnwidth +\vskip-12.5pt +\if@twocolumn\else % one column journal + \divide\rubricwidth by144\multiply\rubricwidth by89 % perform golden section + \vskip-\topskip +\fi +\hrule\@height0.35mm\noindent +\advance\fboxsep by.25mm +\global\advance\rubricwidth by0pt +\rubric +\vss}\vskip19.5pt +% +\if@twocolumn\else + \gdef\footnoterule{% + \kern-3\p@ + \hrule\@width\columnwidth %rubricwidth + \kern2.6\p@} +\fi +% + \setbox\authrun=\vbox\bgroup + \hrule\@height 9mm\@width0\p@ + \pretolerance=10000 + \rightskip=0pt plus 4cm + \nothanksmarks +% \if!\@headnote!\else +% \noindent +% {\LARGE\normalfont\itshape\ignorespaces\@headnote\par}\vskip 3.5mm +% \fi + {\authorfont + \setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }% + \hfuzz=2\textwidth\def\thanks##1{}\@author}% + \setcounter{footnote}{0}% + \global\value{inst}=\value{auth}% + \setcounter{auth}{1}% + \if@twocolumn + \rightskip43mm plus 4cm minus 3mm + \else % one column journal + \rightskip=\linewidth + \advance\rightskip by-\rubricwidth + \advance\rightskip by0pt plus 4cm minus 3mm + \fi +% +\def\and{\unskip\nobreak\enskip{\boldmath$\cdot$}\enskip\ignorespaces}% + \noindent\ignorespaces\@author\vskip7.23pt} + {\LARGE\bfseries + \noindent\ignorespaces + \@title \par}\vskip 11.24pt\relax + \if!\@subtitle!\else + {\large\bfseries + \pretolerance=10000 + \rightskip=0pt plus 3cm + \vskip-5pt + \noindent\ignorespaces\@subtitle \par}\vskip 11.24pt + \fi + \small + \if!\@dedic!\else + \par + \normalsize\it + \addvspace\baselineskip + \noindent\@dedic + \fi + \egroup % end of header box + \@tempdima=\headerboxheight + \advance\@tempdima by-\ht\authrun + \unvbox\authrun + \ifdim\@tempdima>0pt + \vrule width0pt height\@tempdima\par + \fi + \noindent{\small\@date\vskip 6.2mm} + \global\@minipagetrue + \global\everypar{\global\@minipagefalse\global\everypar{}}% +%\vskip22.47pt +} +% +\if@mathematic + \def\vec#1{\ensuremath{\mathchoice + {\mbox{\boldmath$\displaystyle\mathbf{#1}$}} + {\mbox{\boldmath$\textstyle\mathbf{#1}$}} + {\mbox{\boldmath$\scriptstyle\mathbf{#1}$}} + {\mbox{\boldmath$\scriptscriptstyle\mathbf{#1}$}}}} +\else + \def\vec#1{\ensuremath{\mathchoice + {\mbox{\boldmath$\displaystyle#1$}} + {\mbox{\boldmath$\textstyle#1$}} + {\mbox{\boldmath$\scriptstyle#1$}} + {\mbox{\boldmath$\scriptscriptstyle#1$}}}} +\fi +% +\def\tens#1{\ensuremath{\mathsf{#1}}} +% +\setcounter{secnumdepth}{3} +\newcounter {section} +\newcounter {subsection}[section] +\newcounter {subsubsection}[subsection] +\newcounter {paragraph}[subsubsection] +\newcounter {subparagraph}[paragraph] +\renewcommand\thesection {\@arabic\c@section} +\renewcommand\thesubsection {\thesection.\@arabic\c@subsection} +\renewcommand\thesubsubsection{\thesubsection.\@arabic\c@subsubsection} +\renewcommand\theparagraph {\thesubsubsection.\@arabic\c@paragraph} +\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph} +% +\def\@hangfrom#1{\setbox\@tempboxa\hbox{#1}% + \hangindent \z@\noindent\box\@tempboxa} +% +\def\@seccntformat#1{\csname the#1\endcsname\sectcounterend +\hskip\betweenumberspace} +% +\newif\if@sectrule +\if@twocolumn\else\let\@sectruletrue=\relax\fi +\if@avier\let\@sectruletrue=\relax\fi +\def\makesectrule{\if@sectrule\global\@sectrulefalse\null\vglue-\topskip +\hrule\nobreak\parskip=5pt\relax\fi} +% +\let\makesectruleori=\makesectrule +\def\restoresectrule{\global\let\makesectrule=\makesectruleori\global\@sectrulefalse} +\def\nosectrule{\let\makesectrule=\restoresectrule} +% +\def\@startsection#1#2#3#4#5#6{% + \if@noskipsec \leavevmode \fi + \par + \@tempskipa #4\relax + \@afterindenttrue + \ifdim \@tempskipa <\z@ + \@tempskipa -\@tempskipa \@afterindentfalse + \fi + \if@nobreak + \everypar{}% + \else + \addpenalty\@secpenalty\addvspace\@tempskipa + \fi + \ifnum#2=1\relax\@sectruletrue\fi + \@ifstar + {\@ssect{#3}{#4}{#5}{#6}}% + {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}} +% +\def\@sect#1#2#3#4#5#6[#7]#8{% + \ifnum #2>\c@secnumdepth + \let\@svsec\@empty + \else + \refstepcounter{#1}% + \protected@edef\@svsec{\@seccntformat{#1}\relax}% + \fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup + #6{\makesectrule + \@hangfrom{\hskip #3\relax\@svsec}% + \raggedright + \hyphenpenalty \@M% + \interlinepenalty \@M #8\@@par}% + \endgroup + \csname #1mark\endcsname{#7}% + \addcontentsline{toc}{#1}{% + \ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname\sectcounterend}% + \fi + #7}% + \else + \def\@svsechd{% + #6{\hskip #3\relax + \@svsec #8\/\hskip\aftertext}% + \csname #1mark\endcsname{#7}% + \addcontentsline{toc}{#1}{% + \ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}% + \fi + #7}}% + \fi + \@xsect{#5}} +% +\def\@ssect#1#2#3#4#5{% + \@tempskipa #3\relax + \ifdim \@tempskipa>\z@ + \begingroup + #4{\makesectrule + \@hangfrom{\hskip #1}% + \interlinepenalty \@M #5\@@par}% + \endgroup + \else + \def\@svsechd{#4{\hskip #1\relax #5}}% + \fi + \@xsect{#3}} + +% +% measures and setting of sections +% +\def\section{\@startsection{section}{1}{\z@}% + {-21dd plus-8pt minus-4pt}{10.5dd} + {\normalsize\bfseries\boldmath}} +\def\subsection{\@startsection{subsection}{2}{\z@}% + {-21dd plus-8pt minus-4pt}{10.5dd} + {\normalsize\upshape}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-13dd plus-8pt minus-4pt}{10.5dd} + {\normalsize\itshape}} +\def\paragraph{\@startsection{paragraph}{4}{\z@}% + {-13pt plus-8pt minus-4pt}{\z@}{\normalsize\itshape}} + +\setlength\leftmargini {\parindent} +\leftmargin \leftmargini +\setlength\leftmarginii {\parindent} +\setlength\leftmarginiii {1.87em} +\setlength\leftmarginiv {1.7em} +\setlength\leftmarginv {.5em} +\setlength\leftmarginvi {.5em} +\setlength \labelsep {.5em} +\setlength \labelwidth{\leftmargini} +\addtolength\labelwidth{-\labelsep} +\@beginparpenalty -\@lowpenalty +\@endparpenalty -\@lowpenalty +\@itempenalty -\@lowpenalty +\renewcommand\theenumi{\@arabic\c@enumi} +\renewcommand\theenumii{\@alph\c@enumii} +\renewcommand\theenumiii{\@roman\c@enumiii} +\renewcommand\theenumiv{\@Alph\c@enumiv} +\newcommand\labelenumi{\theenumi.} +\newcommand\labelenumii{(\theenumii)} +\newcommand\labelenumiii{\theenumiii.} +\newcommand\labelenumiv{\theenumiv.} +\renewcommand\p@enumii{\theenumi} +\renewcommand\p@enumiii{\theenumi(\theenumii)} +\renewcommand\p@enumiv{\p@enumiii\theenumiii} +\newcommand\labelitemi{\normalfont\bfseries --} +\newcommand\labelitemii{\normalfont\bfseries --} +\newcommand\labelitemiii{$\m@th\bullet$} +\newcommand\labelitemiv{$\m@th\cdot$} + +\if@spthms +% definition of the "\spnewtheorem" command. +% +% Usage: +% +% \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font} +% or \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font} +% or \spnewtheorem*{env_nam}{caption}{cap_font}{body_font} +% +% New is "cap_font" and "body_font". It stands for +% fontdefinition of the caption and the text itself. +% +% "\spnewtheorem*" gives a theorem without number. +% +% A defined spnewthoerem environment is used as described +% by Lamport. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\def\@thmcountersep{} +\def\@thmcounterend{} +\newcommand\nocaption{\noexpand\@gobble} +\newdimen\spthmsep \spthmsep=5pt + +\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}} + +% definition of \spnewtheorem with number + +\def\@spnthm#1#2{% + \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}} +\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}} + +\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}\@addtoreset{#1}{#3}% + \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand + \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}% + \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spothm#1[#2]#3#4#5{% + \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}% + {\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{the#1}{\@nameuse{the#2}}% + \expandafter\xdef\csname #1name\endcsname{#3}% + \global\@namedef{#1}{\@spthm{#2}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}}} + +\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\labelsep=\spthmsep\refstepcounter{#1}% +\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}} + +\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}% + \ignorespaces} + +\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname + the#1\endcsname}{#5}{#3}{#4}\ignorespaces} + +\def\normalthmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist\normalfont + \item[\hskip\labelsep{##3##1\ ##2\@thmcounterend}]##4} +\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{##4(##3)\@thmcounterend\ }##5}} +\normalthmheadings + +\def\reversethmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist\normalfont + \item[\hskip\labelsep{##3##2\ ##1\@thmcounterend}]##4} +\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##2\ ##1}]{##4(##3)\@thmcounterend\ }##5}} + +% definition of \spnewtheorem* without number + +\def\@sthm#1#2{\@Ynthm{#1}{#2}} + +\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}} + +\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces} + +\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1} + {#4}{#2}{#3}\ignorespaces} + +\def\@Begintheorem#1#2#3{#3\trivlist + \item[\hskip\labelsep{#2#1\@thmcounterend}]} + +\def\@Opargbegintheorem#1#2#3#4{#4\trivlist + \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }} + +% initialize theorem environment + +\if@envcntsect + \def\@thmcountersep{.} + \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape} +\else + \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape} + \if@envcntreset + \@addtoreset{theorem}{section} + \else + \@addtoreset{theorem}{chapter} + \fi +\fi + +%definition of divers theorem environments +\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily} +\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily} +\if@envcntsame % all environments like "Theorem" - using its counter + \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}} +\else % all environments with their own counter + \if@envcntsect % show section counter + \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}} + \else % not numbered with section + \if@envcntreset + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{section}} + \else + \let\spn@wtheorem=\@spynthm + \fi + \fi +\fi +% +\let\spdefaulttheorem=\spn@wtheorem +% +\spn@wtheorem{case}{Case}{\itshape}{\rmfamily} +\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily} +\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape} +\spn@wtheorem{definition}{Definition}{\bfseries}{\rmfamily} +\spn@wtheorem{example}{Example}{\itshape}{\rmfamily} +\spn@wtheorem{exercise}{Exercise}{\bfseries}{\rmfamily} +\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape} +\spn@wtheorem{note}{Note}{\itshape}{\rmfamily} +\spn@wtheorem{problem}{Problem}{\bfseries}{\rmfamily} +\spn@wtheorem{property}{Property}{\itshape}{\rmfamily} +\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape} +\spn@wtheorem{question}{Question}{\itshape}{\rmfamily} +\spn@wtheorem{solution}{Solution}{\bfseries}{\rmfamily} +\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily} +% +\newenvironment{theopargself} + {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5} + \def\@Opargbegintheorem##1##2##3##4{##4\trivlist + \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }}}{} +\newenvironment{theopargself*} + {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{\hspace*{-\labelsep}##4##3\@thmcounterend}##5} + \def\@Opargbegintheorem##1##2##3##4{##4\trivlist + \item[\hskip\labelsep{##3##1}]{\hspace*{-\labelsep}##3##2\@thmcounterend}}}{} +% +\fi + +\def\@takefromreset#1#2{% + \def\@tempa{#1}% + \let\@tempd\@elt + \def\@elt##1{% + \def\@tempb{##1}% + \ifx\@tempa\@tempb\else + \@addtoreset{##1}{#2}% + \fi}% + \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname + \expandafter\def\csname cl@#2\endcsname{}% + \@tempc + \let\@elt\@tempd} + +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\else\unskip\quad\fi\squareforqed} +\def\smartqed{\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}} + +% Define `abstract' environment +\def\abstract{\topsep=0pt\partopsep=0pt\parsep=0pt\itemsep=0pt\relax +\trivlist\item[\hskip\labelsep +{\bfseries\abstractname}]\if!\abstractname!\hskip-\labelsep\fi} +\if@twocolumn + \if@avier + \def\endabstract{\endtrivlist\addvspace{5mm}\strich} + \def\strich{\hrule\vskip1ptplus12pt} + \else + \def\endabstract{\endtrivlist\addvspace{3mm}} + \fi +\else +\fi +% +\newenvironment{verse} + {\let\\\@centercr + \list{}{\itemsep \z@ + \itemindent -1.5em% + \listparindent\itemindent + \rightmargin \leftmargin + \advance\leftmargin 1.5em}% + \item\relax} + {\endlist} +\newenvironment{quotation} + {\list{}{\listparindent 1.5em% + \itemindent \listparindent + \rightmargin \leftmargin + \parsep \z@ \@plus\p@}% + \item\relax} + {\endlist} +\newenvironment{quote} + {\list{}{\rightmargin\leftmargin}% + \item\relax} + {\endlist} +\newcommand\appendix{\par\small + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \renewcommand\thesection{\@Alph\c@section}} +\setlength\arraycolsep{1.5\p@} +\setlength\tabcolsep{6\p@} +\setlength\arrayrulewidth{.4\p@} +\setlength\doublerulesep{2\p@} +\setlength\tabbingsep{\labelsep} +\skip\@mpfootins = \skip\footins +\setlength\fboxsep{3\p@} +\setlength\fboxrule{.4\p@} +\renewcommand\theequation{\@arabic\c@equation} +\newcounter{figure} +\renewcommand\thefigure{\@arabic\c@figure} +\def\fps@figure{tbp} +\def\ftype@figure{1} +\def\ext@figure{lof} +\def\fnum@figure{\figurename~\thefigure} +\newenvironment{figure} + {\@float{figure}} + {\end@float} +\newenvironment{figure*} + {\@dblfloat{figure}} + {\end@dblfloat} +\newcounter{table} +\renewcommand\thetable{\@arabic\c@table} +\def\fps@table{tbp} +\def\ftype@table{2} +\def\ext@table{lot} +\def\fnum@table{\tablename~\thetable} +\newenvironment{table} + {\@float{table}} + {\end@float} +\newenvironment{table*} + {\@dblfloat{table}} + {\end@dblfloat} +% +\def \@floatboxreset {% + \reset@font + \small + \@setnobreak + \@setminipage +} +% +\newcommand{\tableheadseprule}{\noalign{\hrule height.375mm}} +% +\newlength\abovecaptionskip +\newlength\belowcaptionskip +\setlength\abovecaptionskip{10\p@} +\setlength\belowcaptionskip{0\p@} +\newcommand\leftlegendglue{} + +\def\fig@type{figure} + +\newdimen\figcapgap\figcapgap=3pt +\newdimen\tabcapgap\tabcapgap=5.5pt + +\@ifundefined{floatlegendstyle}{\def\floatlegendstyle{\bfseries}}{} + +\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\begingroup + \@parboxrestore + \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +\def\capstrut{\vrule\@width\z@\@height\topskip} + +\@ifundefined{captionstyle}{\def\captionstyle{\normalfont\small}}{} + +\long\def\@makecaption#1#2{% + \captionstyle + \ifx\@captype\fig@type + \vskip\figcapgap + \fi + \setbox\@tempboxa\hbox{{\floatlegendstyle #1\floatcounterend}% + \capstrut #2}% + \ifdim \wd\@tempboxa >\hsize + {\floatlegendstyle #1\floatcounterend}\capstrut #2\par + \else + \hbox to\hsize{\leftlegendglue\unhbox\@tempboxa\hfil}% + \fi + \ifx\@captype\fig@type\else + \vskip\tabcapgap + \fi} + +\newdimen\figgap\figgap=1cc +\long\def\@makesidecaption#1#2{% + \parbox[b]{\@tempdimb}{\captionstyle{\floatlegendstyle + #1\floatcounterend}#2}} +\def\sidecaption#1\caption{% +\setbox\@tempboxa=\hbox{#1\unskip}% +\if@twocolumn + \ifdim\hsize<\textwidth\else + \ifdim\wd\@tempboxa<\columnwidth + \typeout{Double column float fits into single column - + ^^Jyou'd better switch the environment. }% + \fi + \fi +\fi +\@tempdimb=\hsize +\advance\@tempdimb by-\figgap +\advance\@tempdimb by-\wd\@tempboxa +\ifdim\@tempdimb<3cm + \typeout{\string\sidecaption: No sufficient room for the legend; + using normal \string\caption. }% + \unhbox\@tempboxa + \let\@capcommand=\@caption +\else + \let\@capcommand=\@sidecaption + \leavevmode + \unhbox\@tempboxa + \hfill +\fi +\refstepcounter\@captype +\@dblarg{\@capcommand\@captype}} + +\long\def\@sidecaption#1[#2]#3{\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\begingroup + \@parboxrestore + \@makesidecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +% Define `acknowledgement' environment +\def\acknowledgement{\par\addvspace{17pt}\small\rmfamily +\trivlist\if!\ackname!\item[]\else +\item[\hskip\labelsep +{\bfseries\ackname}]\fi} +\def\endacknowledgement{\endtrivlist\addvspace{6pt}} +\newenvironment{acknowledgements}{\begin{acknowledgement}} +{\end{acknowledgement}} +% Define `noteadd' environment +\def\noteadd{\par\addvspace{17pt}\small\rmfamily +\trivlist\item[\hskip\labelsep +{\itshape\noteaddname}]} +\def\endnoteadd{\endtrivlist\addvspace{6pt}} + +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} +\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} +\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} +\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal} +\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal} +\newcommand\@pnumwidth{1.55em} +\newcommand\@tocrmarg{2.55em} +\newcommand\@dotsep{4.5} +\setcounter{tocdepth}{1} +\newcommand\tableofcontents{% + \section*{\contentsname}% + \@starttoc{toc}% + \addtocontents{toc}{\begingroup\protect\small}% + \AtEndDocument{\addtocontents{toc}{\endgroup}}% + } +\newcommand*\l@part[2]{% + \ifnum \c@tocdepth >-2\relax + \addpenalty\@secpenalty + \addvspace{2.25em \@plus\p@}% + \begingroup + \setlength\@tempdima{3em}% + \parindent \z@ \rightskip \@pnumwidth + \parfillskip -\@pnumwidth + {\leavevmode + \large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par + \nobreak + \if@compatibility + \global\@nobreaktrue + \everypar{\global\@nobreakfalse\everypar{}}% + \fi + \endgroup + \fi} +\newcommand*\l@section{\@dottedtocline{1}{0pt}{1.5em}} +\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} +\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} +\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} +\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}} +\newcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\listfigurename}% + {\listfigurename}}% + \@starttoc{lof}% + } +\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}} +\newcommand\listoftables{% + \section*{\listtablename + \@mkboth{\listtablename}{\listtablename}}% + \@starttoc{lot}% + } +\let\l@table\l@figure +\newdimen\bibindent +\setlength\bibindent{\parindent} +\def\@biblabel#1{#1.} +\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw + {\let\protect\noexpand + \immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} +\newenvironment{thebibliography}[1] + {\section*{\refname + \@mkboth{\refname}{\refname}}\small + \list{\@biblabel{\@arabic\c@enumiv}}% + {\settowidth\labelwidth{\@biblabel{#1}}% + \leftmargin\labelwidth + \advance\leftmargin\labelsep + \@openbib@code + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{\@arabic\c@enumiv}}% + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} +% +\newcount\@tempcntc +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@ifundefined + {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries + ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% + {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}% + \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne + \@citea\def\@citea{,\hskip0.1em\ignorespaces}\hbox{\csname b@\@citeb\endcsname}% + \else + \advance\@tempcntb\@ne + \ifnum\@tempcntb=\@tempcntc + \else\advance\@tempcntb\m@ne\@citeo + \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}} +\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else + \@citea\def\@citea{,\hskip0.1em\ignorespaces}% + \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else + {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi + \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi} +% +\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em} +\let\@openbib@code\@empty +\newenvironment{theindex} + {\if@twocolumn + \@restonecolfalse + \else + \@restonecoltrue + \fi + \columnseprule \z@ + \columnsep 35\p@ + \twocolumn[\section*{\indexname}]% + \@mkboth{\indexname}{\indexname}% + \thispagestyle{plain}\parindent\z@ + \parskip\z@ \@plus .3\p@\relax + \let\item\@idxitem} + {\if@restonecol\onecolumn\else\clearpage\fi} +\newcommand\@idxitem{\par\hangindent 40\p@} +\newcommand\subitem{\@idxitem \hspace*{20\p@}} +\newcommand\subsubitem{\@idxitem \hspace*{30\p@}} +\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax} + +\if@twocolumn + \renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width\columnwidth + \kern2.6\p@} +\else + \renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width.382\columnwidth + \kern2.6\p@} +\fi +\newcommand\@makefntext[1]{% + \noindent + \hb@xt@\bibindent{\hss\@makefnmark\enspace}#1} +% +\def\trans@english{\switcht@albion} +\def\trans@french{\switcht@francais} +\def\trans@german{\switcht@deutsch} +\newenvironment{translation}[1]{\if!#1!\else +\@ifundefined{selectlanguage}{\csname trans@#1\endcsname}{\selectlanguage{#1}}% +\fi}{} +% languages +% English section +\def\switcht@albion{%\typeout{English spoken.}% + \def\abstractname{Abstract}% + \def\ackname{Acknowledgements}% + \def\andname{and}% + \def\lastandname{, and}% + \def\appendixname{Appendix}% + \def\chaptername{Chapter}% + \def\claimname{Claim}% + \def\conjecturename{Conjecture}% + \def\contentsname{Contents}% + \def\corollaryname{Corollary}% + \def\definitionname{Definition}% + \def\emailname{E-mail}% + \def\examplename{Example}% + \def\exercisename{Exercise}% + \def\figurename{Fig.}% + \def\keywordname{{\bfseries Keywords}}% + \def\indexname{Index}% + \def\lemmaname{Lemma}% + \def\contriblistname{List of Contributors}% + \def\listfigurename{List of Figures}% + \def\listtablename{List of Tables}% + \def\mailname{{\itshape Correspondence to\/}:}% + \def\noteaddname{Note added in proof}% + \def\notename{Note}% + \def\partname{Part}% + \def\problemname{Problem}% + \def\proofname{Proof}% + \def\propertyname{Property}% + \def\questionname{Question}% + \def\refname{References}% + \def\remarkname{Remark}% + \def\seename{see}% + \def\solutionname{Solution}% + \def\tablename{Table}% + \def\theoremname{Theorem}% +}\switcht@albion % make English default +% +% French section +\def\switcht@francais{\svlanginfo +%\typeout{On parle francais.}% + \def\abstractname{R\'esum\'e\runinend}% + \def\ackname{Remerciements\runinend}% + \def\andname{et}% + \def\lastandname{ et}% + \def\appendixname{Appendice}% + \def\chaptername{Chapitre}% + \def\claimname{Pr\'etention}% + \def\conjecturename{Hypoth\`ese}% + \def\contentsname{Table des mati\`eres}% + \def\corollaryname{Corollaire}% + \def\definitionname{D\'efinition}% + \def\emailname{E-mail}% + \def\examplename{Exemple}% + \def\exercisename{Exercice}% + \def\figurename{Fig.}% + \def\keywordname{{\bfseries Mots-cl\'e\runinend}}% + \def\indexname{Index}% + \def\lemmaname{Lemme}% + \def\contriblistname{Liste des contributeurs}% + \def\listfigurename{Liste des figures}% + \def\listtablename{Liste des tables}% + \def\mailname{{\itshape Correspondence to\/}:}% + \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}% + \def\notename{Remarque}% + \def\partname{Partie}% + \def\problemname{Probl\`eme}% + \def\proofname{Preuve}% + \def\propertyname{Caract\'eristique}% +%\def\propositionname{Proposition}% + \def\questionname{Question}% + \def\refname{Bibliographie}% + \def\remarkname{Remarque}% + \def\seename{voyez}% + \def\solutionname{Solution}% +%\def\subclassname{{\it Subject Classifications\/}:}% + \def\tablename{Tableau}% + \def\theoremname{Th\'eor\`eme}% +} +% +% German section +\def\switcht@deutsch{\svlanginfo +%\typeout{Man spricht deutsch.}% + \def\abstractname{Zusammenfassung\runinend}% + \def\ackname{Danksagung\runinend}% + \def\andname{und}% + \def\lastandname{ und}% + \def\appendixname{Anhang}% + \def\chaptername{Kapitel}% + \def\claimname{Behauptung}% + \def\conjecturename{Hypothese}% + \def\contentsname{Inhaltsverzeichnis}% + \def\corollaryname{Korollar}% +%\def\definitionname{Definition}% + \def\emailname{E-Mail}% + \def\examplename{Beispiel}% + \def\exercisename{\"Ubung}% + \def\figurename{Abb.}% + \def\keywordname{{\bfseries Schl\"usselw\"orter\runinend}}% + \def\indexname{Index}% +%\def\lemmaname{Lemma}% + \def\contriblistname{Mitarbeiter}% + \def\listfigurename{Abbildungsverzeichnis}% + \def\listtablename{Tabellenverzeichnis}% + \def\mailname{{\itshape Correspondence to\/}:}% + \def\noteaddname{Nachtrag}% + \def\notename{Anmerkung}% + \def\partname{Teil}% +%\def\problemname{Problem}% + \def\proofname{Beweis}% + \def\propertyname{Eigenschaft}% +%\def\propositionname{Proposition}% + \def\questionname{Frage}% + \def\refname{Literatur}% + \def\remarkname{Anmerkung}% + \def\seename{siehe}% + \def\solutionname{L\"osung}% +%\def\subclassname{{\it Subject Classifications\/}:}% + \def\tablename{Tabelle}% +%\def\theoremname{Theorem}% +} +\newcommand\today{} +\edef\today{\ifcase\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space\number\day, \number\year} +\setlength\columnsep{1.5cc} +\setlength\columnseprule{0\p@} +% +\frenchspacing +\clubpenalty=10000 +\widowpenalty=10000 +\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil +\global\let\@textbottom\relax}} +\pagestyle{headings} +\pagenumbering{arabic} +\if@twocolumn + \twocolumn +\fi +\if@avier + \onecolumn + \setlength{\textwidth}{156mm} + \setlength{\textheight}{226mm} +\fi +\if@referee + \makereferee +\fi +\flushbottom +\endinput +%% +%% End of file `svjour2.cls'. diff --git a/vldb/ingles/vldb.tex b/vldb/ingles/vldb.tex new file mode 100644 index 0000000..807080a --- /dev/null +++ b/vldb/ingles/vldb.tex @@ -0,0 +1,150 @@ +%%%%%%%%%%%%%%%%%%%%%%% 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} diff --git a/vldb/pt/algorithms.tex b/vldb/pt/algorithms.tex new file mode 100755 index 0000000..61d26cd --- /dev/null +++ b/vldb/pt/algorithms.tex @@ -0,0 +1,19 @@ +\section{Os Algoritmos} +\label{sec:thealgorithm} + +\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} diff --git a/vldb/pt/applications.tex b/vldb/pt/applications.tex new file mode 100644 index 0000000..785ccc0 --- /dev/null +++ b/vldb/pt/applications.tex @@ -0,0 +1,2 @@ +\section{Aplica\c{c}\~oes} +\label{sec:applications} \ No newline at end of file diff --git a/vldb/pt/conclusions.tex b/vldb/pt/conclusions.tex new file mode 100755 index 0000000..08f3cd4 --- /dev/null +++ b/vldb/pt/conclusions.tex @@ -0,0 +1,3 @@ +\section{Conclus\~oes} + + diff --git a/vldb/pt/experimentalresults.tex b/vldb/pt/experimentalresults.tex new file mode 100755 index 0000000..5152c0e --- /dev/null +++ b/vldb/pt/experimentalresults.tex @@ -0,0 +1 @@ +\section{Resultados Experimentais} diff --git 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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 diff --git a/vldb/pt/introduction.tex b/vldb/pt/introduction.tex new file mode 100755 index 0000000..bf4ef85 --- /dev/null +++ b/vldb/pt/introduction.tex @@ -0,0 +1,13 @@ +\section{Introdu\c{c}\~ao} +\label{sec:introduction} +% 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*} + diff --git a/vldb/pt/makefile b/vldb/pt/makefile new file mode 100755 index 0000000..c1a738f --- /dev/null +++ b/vldb/pt/makefile @@ -0,0 +1,17 @@ +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 + diff --git a/vldb/pt/references.bib b/vldb/pt/references.bib new file mode 100755 index 0000000..6f54cbe --- /dev/null +++ b/vldb/pt/references.bib @@ -0,0 +1,669 @@ +@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} +} + +@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�os para a Constru�o de Arquivos invertidos}, + school = {Departamento de Ci�cia da Computa�o, Universidade Federal de Minas Gerais}, + year = 2000, + month = {Mar�}, + 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�es em Pascal e C}, + publisher = {Pioneira Thompson}, + year = 2004, + edition = {segunda edi�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}, + year = {1980}, + 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 = {}, + 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)}, +} + diff --git a/vldb/pt/relatedwork.tex b/vldb/pt/relatedwork.tex new file mode 100755 index 0000000..554b9db --- /dev/null +++ b/vldb/pt/relatedwork.tex @@ -0,0 +1,2 @@ +\section{Trabalhos Relacionados} +\cite{bkz05} \ No newline at end of file diff --git a/vldb/pt/svglov2.clo b/vldb/pt/svglov2.clo new file mode 100644 index 0000000..d98306e --- /dev/null +++ b/vldb/pt/svglov2.clo @@ -0,0 +1,77 @@ +% 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 \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% 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{% +\string} in preambel^^J}}{}} +% +\endinput +%% +%% End of file `svglov2.clo'. diff --git a/vldb/pt/svjour2.cls b/vldb/pt/svjour2.cls new file mode 100644 index 0000000..56d9216 --- /dev/null +++ b/vldb/pt/svjour2.cls @@ -0,0 +1,1419 @@ +% SVJour2 DOCUMENT CLASS -- version 2.8 for LaTeX2e +% +% LaTeX 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 \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{svjour2}[2005/08/29 v2.8 +^^JLaTeX document class for Springer journals] +\newcommand\@ptsize{} +\newif\if@restonecol +\newif\if@titlepage +\@titlepagefalse +\DeclareOption{a4paper} + {\setlength\paperheight {297mm}% + \setlength\paperwidth {210mm}} +\DeclareOption{10pt}{\renewcommand\@ptsize{0}} +\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue} +\DeclareOption{draft}{\setlength\overfullrule{5pt}} +\DeclareOption{final}{\setlength\overfullrule{0pt}} +\DeclareOption{fleqn}{\input{fleqn.clo}\AtBeginDocument{\mathindent\z@}} +\DeclareOption{twocolumn}{\@twocolumntrue\ExecuteOptions{fleqn}} +\newif\if@avier\@avierfalse +\DeclareOption{onecollarge}{\@aviertrue} +\let\if@mathematic\iftrue +\let\if@numbook\iffalse +\DeclareOption{numbook}{\let\if@envcntsect\iftrue + \AtEndOfPackage{% + \renewcommand\thefigure{\thesection.\@arabic\c@figure}% + \renewcommand\thetable{\thesection.\@arabic\c@table}% + \renewcommand\theequation{\thesection.\@arabic\c@equation}% + \@addtoreset{figure}{section}% + \@addtoreset{table}{section}% + \@addtoreset{equation}{section}% + }% +} +\DeclareOption{openbib}{% + \AtEndOfPackage{% + \renewcommand\@openbib@code{% + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + }% + \renewcommand\newblock{\par}}% +} +\DeclareOption{natbib}{% +\AtEndOfClass{\RequirePackage{natbib}% +% Changing some parameters of NATBIB +\setlength{\bibhang}{\parindent}% +%\setlength{\bibsep}{0mm}% +\let\bibfont=\small +\def\@biblabel#1{#1.}% +\newcommand{\etal}{et al.}% +\bibpunct{(}{)}{;}{a}{}{,}}} +% +\let\if@runhead\iffalse +\DeclareOption{runningheads}{\let\if@runhead\iftrue} +\let\if@smartrunh\iffalse +\DeclareOption{smartrunhead}{\let\if@smartrunh\iftrue} +\DeclareOption{nosmartrunhead}{\let\if@smartrunh\iffalse} +\let\if@envcntreset\iffalse +\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue} +\let\if@envcntsame\iffalse +\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue} +\let\if@envcntsect\iffalse +\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue} +\let\if@referee\iffalse +\DeclareOption{referee}{\let\if@referee\iftrue} +\def\makereferee{\def\baselinestretch{2}} +\let\if@instindent\iffalse +\DeclareOption{instindent}{\let\if@instindent\iftrue} +\let\if@smartand\iffalse +\DeclareOption{smartand}{\let\if@smartand\iftrue} +\let\if@spthms\iftrue +\DeclareOption{nospthms}{\let\if@spthms\iffalse} +% +% language and babel dependencies +\DeclareOption{deutsch}{\def\switcht@@therlang{\switcht@deutsch}% +\gdef\svlanginfo{\typeout{Man spricht deutsch.}\global\let\svlanginfo\relax}} +\DeclareOption{francais}{\def\switcht@@therlang{\switcht@francais}% +\gdef\svlanginfo{\typeout{On parle francais.}\global\let\svlanginfo\relax}} +\let\switcht@@therlang\relax +\let\svlanginfo\relax +% +\AtBeginDocument{\@ifpackageloaded{babel}{% +\@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}% +\@ifundefined{extrasUKenglish}{}{\addto\extrasUKenglish{\switcht@albion}}% +\@ifundefined{extrasfrenchb}{}{\addto\extrasfrenchb{\switcht@francais}}% +\@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}% +\@ifundefined{extrasngerman}{}{\addto\extrasngerman{\switcht@deutsch}}% +}{\switcht@@therlang}% +} +% +\def\ClassInfoNoLine#1#2{% + \ClassInfo{#1}{#2\@gobble}% +} +\let\journalopt\@empty +\DeclareOption*{% +\InputIfFileExists{sv\CurrentOption.clo}{% +\global\let\journalopt\CurrentOption}{% +\ClassWarning{Springer-SVJour2}{Specified option or subpackage +"\CurrentOption" not found -}\OptionNotUsed}} +\ExecuteOptions{a4paper,twoside,10pt,instindent} +\ProcessOptions +% +\ifx\journalopt\@empty\relax +\ClassInfoNoLine{Springer-SVJour2}{extra/valid Springer sub-package (-> *.clo) +\MessageBreak not found in option list of \string\documentclass +\MessageBreak - autoactivating "global" style}{} +\input{svglov2.clo} +\else +\@ifundefined{validfor}{% +\ClassError{Springer-SVJour2}{Possible option clash for sub-package +\MessageBreak "sv\journalopt.clo" - option file not valid +\MessageBreak for this class}{Perhaps you used an option of the old +Springer class SVJour!} +}{} +\fi +% +\if@smartrunh\AtEndDocument{\islastpageeven\getlastpagenumber}\fi +% +\newcommand{\twocoltest}[2]{\if@twocolumn\def\@gtempa{#2}\else\def\@gtempa{#1}\fi +\@gtempa\makeatother} +\newcommand{\columncase}{\makeatletter\twocoltest} +% +\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00} +\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01} +\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02} +\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03} +\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04} +\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05} +\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06} +\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07} +\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08} +\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09} +\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A} +% +\setlength\parindent{15\p@} +\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@} +\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@} +\setlength\headheight{12\p@} +\setlength\headsep {16.74dd} +\setlength\topskip {10\p@} +\setlength\footskip{30\p@} +\setlength\maxdepth{.5\topskip} +% +\@settopoint\textwidth +\setlength\marginparsep {10\p@} +\setlength\marginparpush{5\p@} +\setlength\topmargin{-10pt} +\if@twocolumn + \setlength\oddsidemargin {-30\p@} + \setlength\evensidemargin{-30\p@} +\else + \setlength\oddsidemargin {\z@} + \setlength\evensidemargin{\z@} +\fi +\setlength\marginparwidth {48\p@} +\setlength\footnotesep{8\p@} +\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@} +\setlength\floatsep {12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\textfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@} +\setlength\intextsep {20\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\dblfloatsep {12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@} +\setlength\@fptop{0\p@} +\setlength\@fpsep{12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\@fpbot{0\p@ \@plus 1fil} +\setlength\@dblfptop{0\p@} +\setlength\@dblfpsep{12\p@ \@plus 2\p@ \@minus 2\p@} +\setlength\@dblfpbot{0\p@ \@plus 1fil} +\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@} +\def\@listi{\leftmargin\leftmargini + \parsep \z@ + \topsep 6\p@ \@plus2\p@ \@minus4\p@ + \itemsep\parsep} +\let\@listI\@listi +\@listi +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep \z@ + \parsep \topsep + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep \z@ + \parsep \topsep + \itemsep \parsep} +\def\@listiv {\leftmargin\leftmarginiv + \labelwidth\leftmarginiv + \advance\labelwidth-\labelsep} +\def\@listv {\leftmargin\leftmarginv + \labelwidth\leftmarginv + \advance\labelwidth-\labelsep} +\def\@listvi {\leftmargin\leftmarginvi + \labelwidth\leftmarginvi + \advance\labelwidth-\labelsep} +% +\setlength\lineskip{1\p@} +\setlength\normallineskip{1\p@} +\renewcommand\baselinestretch{} +\setlength\parskip{0\p@ \@plus \p@} +\@lowpenalty 51 +\@medpenalty 151 +\@highpenalty 301 +\setcounter{topnumber}{4} +\renewcommand\topfraction{.9} +\setcounter{bottomnumber}{2} +\renewcommand\bottomfraction{.7} +\setcounter{totalnumber}{6} +\renewcommand\textfraction{.1} +\renewcommand\floatpagefraction{.85} +\setcounter{dbltopnumber}{3} +\renewcommand\dbltopfraction{.85} +\renewcommand\dblfloatpagefraction{.85} +\def\ps@headings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\small\csname runheadhook\endcsname + \rlap{\thepage}\hfil\leftmark\unskip}% + \def\@oddhead{\small\csname runheadhook\endcsname + \ignorespaces\rightmark\hfil\llap{\thepage}}% + \let\@mkboth\@gobbletwo + \let\sectionmark\@gobble + \let\subsectionmark\@gobble + } +% make indentations changeable +\def\setitemindent#1{\settowidth{\labelwidth}{#1}% + \leftmargini\labelwidth + \advance\leftmargini\labelsep + \def\@listi{\leftmargin\leftmargini + \labelwidth\leftmargini\advance\labelwidth by -\labelsep + \parsep=\parskip + \topsep=\medskipamount + \itemsep=\parskip \advance\itemsep by -\parsep}} +\def\setitemitemindent#1{\settowidth{\labelwidth}{#1}% + \leftmarginii\labelwidth + \advance\leftmarginii\labelsep +\def\@listii{\leftmargin\leftmarginii + \labelwidth\leftmarginii\advance\labelwidth by -\labelsep + \parsep=\parskip + \topsep=\z@ + \itemsep=\parskip \advance\itemsep by -\parsep}} +% labels of description +\def\descriptionlabel#1{\hspace\labelsep #1\hfil} +% adjusted environment "description" +% if an optional parameter (at the first two levels of lists) +% is present, its width is considered to be the widest mark +% throughout the current list. +\def\description{\@ifnextchar[{\@describe}{\list{}{\labelwidth\z@ + \itemindent-\leftmargin \let\makelabel\descriptionlabel}}} +\let\enddescription\endlist +% +\def\describelabel#1{#1\hfil} +\def\@describe[#1]{\relax\ifnum\@listdepth=0 +\setitemindent{#1}\else\ifnum\@listdepth=1 +\setitemitemindent{#1}\fi\fi +\list{--}{\let\makelabel\describelabel}} +% +\newdimen\logodepth +\logodepth=1.2cm +\newdimen\headerboxheight +\headerboxheight=180pt % 18 10.5dd-lines - 2\baselineskip +\advance\headerboxheight by-14.5mm +\newdimen\betweenumberspace % dimension for space between +\betweenumberspace=3.33pt % number and text of titles. +\newdimen\aftertext % dimension for space after +\aftertext=5pt % text of title. +\newdimen\headlineindent % dimension for space between +\headlineindent=1.166cm % number and text of headings. +\if@mathematic + \def\runinend{} % \enspace} + \def\floatcounterend{\enspace} + \def\sectcounterend{} +\else + \def\runinend{.} + \def\floatcounterend{.\ } + \def\sectcounterend{.} +\fi +\def\email#1{\emailname: #1} +\def\keywords#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\keywordname\enspace\ignorespaces#1\par}} +% +\def\subclassname{{\bfseries Mathematics Subject Classification +(2000)}\enspace} +\def\subclass#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\subclassname\ignorespaces#1\par}} +% +\def\PACSname{\textbf{PACS}\enspace} +\def\PACS#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\PACSname\ignorespaces#1\par}} +% +\def\CRclassname{{\bfseries CR Subject Classification}\enspace} +\def\CRclass#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\CRclassname\ignorespaces#1\par}} +% +\def\ESMname{\textbf{Electronic Supplementary Material}\enspace} +\def\ESM#1{\par\addvspace\medskipamount +\noindent\ESMname\ignorespaces#1\par} +% +\newcounter{inst} +\newcounter{auth} +\def\authdepth{2} +\newdimen\instindent +\newbox\authrun +\newtoks\authorrunning +\newbox\titrun +\newtoks\titlerunning +\def\authorfont{\bfseries} + +\def\combirunning#1{\gdef\@combi{#1}} +\def\@combi{} +\newbox\combirun +% +\def\ps@last{\def\@evenhead{\small\rlap{\thepage}\hfil +\lastevenhead}} +\newcounter{lastpage} +\def\islastpageeven{\@ifundefined{lastpagenumber} +{\setcounter{lastpage}{0}}{\setcounter{lastpage}{\lastpagenumber}} +\ifnum\value{lastpage}>0 + \ifodd\value{lastpage}% + \else + \if@smartrunh + \thispagestyle{last}% + \fi + \fi +\fi} +\def\getlastpagenumber{\clearpage +\addtocounter{page}{-1}% + \immediate\write\@auxout{\string\gdef\string\lastpagenumber{\thepage}}% + \immediate\write\@auxout{\string\newlabel{LastPage}{{}{\thepage}}}% + \addtocounter{page}{1}} + +\def\journalname#1{\gdef\@journalname{#1}} + +\def\dedication#1{\gdef\@dedic{#1}} +\def\@dedic{} + +\let\@date\undefined +\def\notused{~} + +\def\institute#1{\gdef\@institute{#1}} + +\def\offprints#1{\begingroup +\def\protect{\noexpand\protect\noexpand}\xdef\@thanks{\@thanks +\protect\footnotetext[0]{\unskip\hskip-15pt{\itshape Send offprint requests +to\/}: \ignorespaces#1}}\endgroup\ignorespaces} + +%\def\mail#1{\gdef\@mail{#1}} +%\def\@mail{} + +\def\@thanks{} + +\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}% + \or \dagger\or \ddagger\or + \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger + \or \ddagger\ddagger \else\@ctrerr\fi\relax} +% +%\def\invthanks#1{\footnotetext[0]{\kern-\bibindent#1}} +% +\def\nothanksmarks{\def\thanks##1{\protected@xdef\@thanks{\@thanks + \protect\footnotetext[0]{\kern-\bibindent##1}}}} +% +\def\subtitle#1{\gdef\@subtitle{#1}} +\def\@subtitle{} + +\def\headnote#1{\gdef\@headnote{#1}} +\def\@headnote{} + +\def\papertype#1{\gdef\paper@type{\MakeUppercase{#1}}} +\def\paper@type{} + +\def\ch@ckobl#1#2{\@ifundefined{@#1} + {\typeout{SVJour2 warning: Missing +\expandafter\string\csname#1\endcsname}% + \csname #1\endcsname{#2}} + {}} +% +\def\ProcessRunnHead{% + \def\\{\unskip\ \ignorespaces}% + \def\thanks##1{\unskip{}}% + \instindent=\textwidth + \advance\instindent by-\headlineindent + \if!\the\titlerunning!\else + \edef\@title{\the\titlerunning}% + \fi + \global\setbox\titrun=\hbox{\small\rmfamily\unboldmath\ignorespaces\@title + \unskip}% + \ifdim\wd\titrun>\instindent + \typeout{^^JSVJour2 Warning: Title too long for running head.}% + \typeout{Please supply a shorter form with \string\titlerunning + \space prior to \string\maketitle}% + \global\setbox\titrun=\hbox{\small\rmfamily + Title Suppressed Due to Excessive Length}% + \fi + \xdef\@title{\copy\titrun}% +% + \if!\the\authorrunning! + \else + \setcounter{auth}{1}% + \edef\@author{\the\authorrunning}% + \fi + \ifnum\value{inst}>\authdepth + \def\stripauthor##1\and##2\endauthor{% + \protected@xdef\@author{##1\unskip\unskip\if!##2!\else\ et al.\fi}}% + \expandafter\stripauthor\@author\and\endauthor + \else + \gdef\and{\unskip, \ignorespaces}% + {\def\and{\noexpand\protect\noexpand\and}% + \protected@xdef\@author{\@author}} + \fi + \global\setbox\authrun=\hbox{\small\rmfamily\unboldmath\ignorespaces + \@author\unskip}% + \ifdim\wd\authrun>\instindent + \typeout{^^JSVJour2 Warning: Author name(s) too long for running head. + ^^JPlease supply a shorter form with \string\authorrunning + \space prior to \string\maketitle}% + \global\setbox\authrun=\hbox{\small\rmfamily Please give a shorter version + with: {\tt\string\authorrunning\space and + \string\titlerunning\space prior to \string\maketitle}}% + \fi + \xdef\@author{\copy\authrun}% + \markboth{\@author}{\@title}% +} +% +\let\orithanks=\thanks +\def\thanks#1{\ClassWarning{SVJour2}{\string\thanks\space may only be +used inside of \string\title, \string\author,\MessageBreak +and \string\date\space prior to \string\maketitle}} +% +\def\maketitle{\par\let\thanks=\orithanks +\ch@ckobl{journalname}{Noname} +\ch@ckobl{date}{the date of receipt and acceptance should be inserted +later} +\ch@ckobl{title}{A title should be given} +\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given} +\ch@ckobl{institute}{Address(es) of author(s) should be given} +\begingroup +% + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \def\@makefnmark{$^{\@thefnmark}$}% + \renewcommand\@makefntext[1]{% + \noindent + \hb@xt@\bibindent{\hss\@makefnmark\enspace}##1\vrule height0pt + width0pt depth8pt} +% + \def\lastand{\ifnum\value{inst}=2\relax + \unskip{} \andname\ + \else + \unskip, \andname\ + \fi}% + \def\and{\stepcounter{auth}\relax + \if@smartand + \ifnum\value{auth}=\value{inst}% + \lastand + \else + \unskip, + \fi + \else + \unskip, + \fi}% + \thispagestyle{empty} + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi +% + \global\@topnum\z@ + \if!\@thanks!\else + \@thanks +\insert\footins{\vskip-3pt\hrule width\columnwidth\vskip3pt}% + \fi + {\def\thanks##1{\unskip{}}% + \def\iand{\\[5pt]\let\and=\nand}% + \def\nand{\ifhmode\unskip\nobreak\fi\ $\cdot$ }% + \let\and=\nand + \def\at{\\\let\and=\iand}% + \footnotetext[0]{\kern-\bibindent + \ignorespaces\@institute}\vspace{5dd}}% +%\if!\@mail!\else +% \footnotetext[0]{\kern-\bibindent\mailname\ +% \ignorespaces\@mail}% +%\fi +% + \if@runhead + \ProcessRunnHead + \fi +% + \endgroup + \setcounter{footnote}{0} + \global\let\thanks\relax + \global\let\maketitle\relax + \global\let\@maketitle\relax + \global\let\@thanks\@empty + \global\let\@author\@empty + \global\let\@date\@empty + \global\let\@title\@empty + \global\let\@subtitle\@empty + \global\let\title\relax + \global\let\author\relax + \global\let\date\relax + \global\let\and\relax} + +\def\makeheadbox{{% +\hbox to0pt{\vbox{\baselineskip=10dd\hrule\hbox +to\hsize{\vrule\kern3pt\vbox{\kern3pt +\hbox{\bfseries\@journalname\ manuscript No.} +\hbox{(will be inserted by the editor)} +\kern3pt}\hfil\kern3pt\vrule}\hrule}% +\hss}}} +% +\def\rubric{\setbox0=\hbox{\small\strut}\@tempdima=\ht0\advance +\@tempdima\dp0\advance\@tempdima2\fboxsep\vrule\@height\@tempdima +\@width\z@} +\newdimen\rubricwidth +% +\def\@maketitle{\newpage +\normalfont +\vbox to0pt{\if@twocolumn\vskip-39pt\else\vskip-49pt\fi +\nointerlineskip +\makeheadbox\vss}\nointerlineskip +\vbox to 0pt{\offinterlineskip\rubricwidth=\columnwidth +\vskip-12.5pt +\if@twocolumn\else % one column journal + \divide\rubricwidth by144\multiply\rubricwidth by89 % perform golden section + \vskip-\topskip +\fi +\hrule\@height0.35mm\noindent +\advance\fboxsep by.25mm +\global\advance\rubricwidth by0pt +\rubric +\vss}\vskip19.5pt +% +\if@twocolumn\else + \gdef\footnoterule{% + \kern-3\p@ + \hrule\@width\columnwidth %rubricwidth + \kern2.6\p@} +\fi +% + \setbox\authrun=\vbox\bgroup + \hrule\@height 9mm\@width0\p@ + \pretolerance=10000 + \rightskip=0pt plus 4cm + \nothanksmarks +% \if!\@headnote!\else +% \noindent +% {\LARGE\normalfont\itshape\ignorespaces\@headnote\par}\vskip 3.5mm +% \fi + {\authorfont + \setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }% + \hfuzz=2\textwidth\def\thanks##1{}\@author}% + \setcounter{footnote}{0}% + \global\value{inst}=\value{auth}% + \setcounter{auth}{1}% + \if@twocolumn + \rightskip43mm plus 4cm minus 3mm + \else % one column journal + \rightskip=\linewidth + \advance\rightskip by-\rubricwidth + \advance\rightskip by0pt plus 4cm minus 3mm + \fi +% +\def\and{\unskip\nobreak\enskip{\boldmath$\cdot$}\enskip\ignorespaces}% + \noindent\ignorespaces\@author\vskip7.23pt} + {\LARGE\bfseries + \noindent\ignorespaces + \@title \par}\vskip 11.24pt\relax + \if!\@subtitle!\else + {\large\bfseries + \pretolerance=10000 + \rightskip=0pt plus 3cm + \vskip-5pt + \noindent\ignorespaces\@subtitle \par}\vskip 11.24pt + \fi + \small + \if!\@dedic!\else + \par + \normalsize\it + \addvspace\baselineskip + \noindent\@dedic + \fi + \egroup % end of header box + \@tempdima=\headerboxheight + \advance\@tempdima by-\ht\authrun + \unvbox\authrun + \ifdim\@tempdima>0pt + \vrule width0pt height\@tempdima\par + \fi + \noindent{\small\@date\vskip 6.2mm} + \global\@minipagetrue + \global\everypar{\global\@minipagefalse\global\everypar{}}% +%\vskip22.47pt +} +% +\if@mathematic + \def\vec#1{\ensuremath{\mathchoice + {\mbox{\boldmath$\displaystyle\mathbf{#1}$}} + {\mbox{\boldmath$\textstyle\mathbf{#1}$}} + {\mbox{\boldmath$\scriptstyle\mathbf{#1}$}} + {\mbox{\boldmath$\scriptscriptstyle\mathbf{#1}$}}}} +\else + \def\vec#1{\ensuremath{\mathchoice + {\mbox{\boldmath$\displaystyle#1$}} + {\mbox{\boldmath$\textstyle#1$}} + {\mbox{\boldmath$\scriptstyle#1$}} + {\mbox{\boldmath$\scriptscriptstyle#1$}}}} +\fi +% +\def\tens#1{\ensuremath{\mathsf{#1}}} +% +\setcounter{secnumdepth}{3} +\newcounter {section} +\newcounter {subsection}[section] +\newcounter {subsubsection}[subsection] +\newcounter {paragraph}[subsubsection] +\newcounter {subparagraph}[paragraph] +\renewcommand\thesection {\@arabic\c@section} +\renewcommand\thesubsection {\thesection.\@arabic\c@subsection} +\renewcommand\thesubsubsection{\thesubsection.\@arabic\c@subsubsection} +\renewcommand\theparagraph {\thesubsubsection.\@arabic\c@paragraph} +\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph} +% +\def\@hangfrom#1{\setbox\@tempboxa\hbox{#1}% + \hangindent \z@\noindent\box\@tempboxa} +% +\def\@seccntformat#1{\csname the#1\endcsname\sectcounterend +\hskip\betweenumberspace} +% +\newif\if@sectrule +\if@twocolumn\else\let\@sectruletrue=\relax\fi +\if@avier\let\@sectruletrue=\relax\fi +\def\makesectrule{\if@sectrule\global\@sectrulefalse\null\vglue-\topskip +\hrule\nobreak\parskip=5pt\relax\fi} +% +\let\makesectruleori=\makesectrule +\def\restoresectrule{\global\let\makesectrule=\makesectruleori\global\@sectrulefalse} +\def\nosectrule{\let\makesectrule=\restoresectrule} +% +\def\@startsection#1#2#3#4#5#6{% + \if@noskipsec \leavevmode \fi + \par + \@tempskipa #4\relax + \@afterindenttrue + \ifdim \@tempskipa <\z@ + \@tempskipa -\@tempskipa \@afterindentfalse + \fi + \if@nobreak + \everypar{}% + \else + \addpenalty\@secpenalty\addvspace\@tempskipa + \fi + \ifnum#2=1\relax\@sectruletrue\fi + \@ifstar + {\@ssect{#3}{#4}{#5}{#6}}% + {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}} +% +\def\@sect#1#2#3#4#5#6[#7]#8{% + \ifnum #2>\c@secnumdepth + \let\@svsec\@empty + \else + \refstepcounter{#1}% + \protected@edef\@svsec{\@seccntformat{#1}\relax}% + \fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup + #6{\makesectrule + \@hangfrom{\hskip #3\relax\@svsec}% + \raggedright + \hyphenpenalty \@M% + \interlinepenalty \@M #8\@@par}% + \endgroup + \csname #1mark\endcsname{#7}% + \addcontentsline{toc}{#1}{% + \ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname\sectcounterend}% + \fi + #7}% + \else + \def\@svsechd{% + #6{\hskip #3\relax + \@svsec #8\/\hskip\aftertext}% + \csname #1mark\endcsname{#7}% + \addcontentsline{toc}{#1}{% + \ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}% + \fi + #7}}% + \fi + \@xsect{#5}} +% +\def\@ssect#1#2#3#4#5{% + \@tempskipa #3\relax + \ifdim \@tempskipa>\z@ + \begingroup + #4{\makesectrule + \@hangfrom{\hskip #1}% + \interlinepenalty \@M #5\@@par}% + \endgroup + \else + \def\@svsechd{#4{\hskip #1\relax #5}}% + \fi + \@xsect{#3}} + +% +% measures and setting of sections +% +\def\section{\@startsection{section}{1}{\z@}% + {-21dd plus-8pt minus-4pt}{10.5dd} + {\normalsize\bfseries\boldmath}} +\def\subsection{\@startsection{subsection}{2}{\z@}% + {-21dd plus-8pt minus-4pt}{10.5dd} + {\normalsize\upshape}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-13dd plus-8pt minus-4pt}{10.5dd} + {\normalsize\itshape}} +\def\paragraph{\@startsection{paragraph}{4}{\z@}% + {-13pt plus-8pt minus-4pt}{\z@}{\normalsize\itshape}} + +\setlength\leftmargini {\parindent} +\leftmargin \leftmargini +\setlength\leftmarginii {\parindent} +\setlength\leftmarginiii {1.87em} +\setlength\leftmarginiv {1.7em} +\setlength\leftmarginv {.5em} +\setlength\leftmarginvi {.5em} +\setlength \labelsep {.5em} +\setlength \labelwidth{\leftmargini} +\addtolength\labelwidth{-\labelsep} +\@beginparpenalty -\@lowpenalty +\@endparpenalty -\@lowpenalty +\@itempenalty -\@lowpenalty +\renewcommand\theenumi{\@arabic\c@enumi} +\renewcommand\theenumii{\@alph\c@enumii} +\renewcommand\theenumiii{\@roman\c@enumiii} +\renewcommand\theenumiv{\@Alph\c@enumiv} +\newcommand\labelenumi{\theenumi.} +\newcommand\labelenumii{(\theenumii)} +\newcommand\labelenumiii{\theenumiii.} +\newcommand\labelenumiv{\theenumiv.} +\renewcommand\p@enumii{\theenumi} +\renewcommand\p@enumiii{\theenumi(\theenumii)} +\renewcommand\p@enumiv{\p@enumiii\theenumiii} +\newcommand\labelitemi{\normalfont\bfseries --} +\newcommand\labelitemii{\normalfont\bfseries --} +\newcommand\labelitemiii{$\m@th\bullet$} +\newcommand\labelitemiv{$\m@th\cdot$} + +\if@spthms +% definition of the "\spnewtheorem" command. +% +% Usage: +% +% \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font} +% or \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font} +% or \spnewtheorem*{env_nam}{caption}{cap_font}{body_font} +% +% New is "cap_font" and "body_font". It stands for +% fontdefinition of the caption and the text itself. +% +% "\spnewtheorem*" gives a theorem without number. +% +% A defined spnewthoerem environment is used as described +% by Lamport. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\def\@thmcountersep{} +\def\@thmcounterend{} +\newcommand\nocaption{\noexpand\@gobble} +\newdimen\spthmsep \spthmsep=5pt + +\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}} + +% definition of \spnewtheorem with number + +\def\@spnthm#1#2{% + \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}} +\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}} + +\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}\@addtoreset{#1}{#3}% + \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand + \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}% + \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spothm#1[#2]#3#4#5{% + \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}% + {\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{the#1}{\@nameuse{the#2}}% + \expandafter\xdef\csname #1name\endcsname{#3}% + \global\@namedef{#1}{\@spthm{#2}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}}} + +\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\labelsep=\spthmsep\refstepcounter{#1}% +\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}} + +\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}% + \ignorespaces} + +\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname + the#1\endcsname}{#5}{#3}{#4}\ignorespaces} + +\def\normalthmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist\normalfont + \item[\hskip\labelsep{##3##1\ ##2\@thmcounterend}]##4} +\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{##4(##3)\@thmcounterend\ }##5}} +\normalthmheadings + +\def\reversethmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist\normalfont + \item[\hskip\labelsep{##3##2\ ##1\@thmcounterend}]##4} +\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##2\ ##1}]{##4(##3)\@thmcounterend\ }##5}} + +% definition of \spnewtheorem* without number + +\def\@sthm#1#2{\@Ynthm{#1}{#2}} + +\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}} + +\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces} + +\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1} + {#4}{#2}{#3}\ignorespaces} + +\def\@Begintheorem#1#2#3{#3\trivlist + \item[\hskip\labelsep{#2#1\@thmcounterend}]} + +\def\@Opargbegintheorem#1#2#3#4{#4\trivlist + \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }} + +% initialize theorem environment + +\if@envcntsect + \def\@thmcountersep{.} + \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape} +\else + \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape} + \if@envcntreset + \@addtoreset{theorem}{section} + \else + \@addtoreset{theorem}{chapter} + \fi +\fi + +%definition of divers theorem environments +\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily} +\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily} +\if@envcntsame % all environments like "Theorem" - using its counter + \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}} +\else % all environments with their own counter + \if@envcntsect % show section counter + \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}} + \else % not numbered with section + \if@envcntreset + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{section}} + \else + \let\spn@wtheorem=\@spynthm + \fi + \fi +\fi +% +\let\spdefaulttheorem=\spn@wtheorem +% +\spn@wtheorem{case}{Case}{\itshape}{\rmfamily} +\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily} +\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape} +\spn@wtheorem{definition}{Definition}{\bfseries}{\rmfamily} +\spn@wtheorem{example}{Example}{\itshape}{\rmfamily} +\spn@wtheorem{exercise}{Exercise}{\bfseries}{\rmfamily} +\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape} +\spn@wtheorem{note}{Note}{\itshape}{\rmfamily} +\spn@wtheorem{problem}{Problem}{\bfseries}{\rmfamily} +\spn@wtheorem{property}{Property}{\itshape}{\rmfamily} +\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape} +\spn@wtheorem{question}{Question}{\itshape}{\rmfamily} +\spn@wtheorem{solution}{Solution}{\bfseries}{\rmfamily} +\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily} +% +\newenvironment{theopargself} + {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5} + \def\@Opargbegintheorem##1##2##3##4{##4\trivlist + \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }}}{} +\newenvironment{theopargself*} + {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{\hspace*{-\labelsep}##4##3\@thmcounterend}##5} + \def\@Opargbegintheorem##1##2##3##4{##4\trivlist + \item[\hskip\labelsep{##3##1}]{\hspace*{-\labelsep}##3##2\@thmcounterend}}}{} +% +\fi + +\def\@takefromreset#1#2{% + \def\@tempa{#1}% + \let\@tempd\@elt + \def\@elt##1{% + \def\@tempb{##1}% + \ifx\@tempa\@tempb\else + \@addtoreset{##1}{#2}% + \fi}% + \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname + \expandafter\def\csname cl@#2\endcsname{}% + \@tempc + \let\@elt\@tempd} + +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\else\unskip\quad\fi\squareforqed} +\def\smartqed{\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}} + +% Define `abstract' environment +\def\abstract{\topsep=0pt\partopsep=0pt\parsep=0pt\itemsep=0pt\relax +\trivlist\item[\hskip\labelsep +{\bfseries\abstractname}]\if!\abstractname!\hskip-\labelsep\fi} +\if@twocolumn + \if@avier + \def\endabstract{\endtrivlist\addvspace{5mm}\strich} + \def\strich{\hrule\vskip1ptplus12pt} + \else + \def\endabstract{\endtrivlist\addvspace{3mm}} + \fi +\else +\fi +% +\newenvironment{verse} + {\let\\\@centercr + \list{}{\itemsep \z@ + \itemindent -1.5em% + \listparindent\itemindent + \rightmargin \leftmargin + \advance\leftmargin 1.5em}% + \item\relax} + {\endlist} +\newenvironment{quotation} + {\list{}{\listparindent 1.5em% + \itemindent \listparindent + \rightmargin \leftmargin + \parsep \z@ \@plus\p@}% + \item\relax} + {\endlist} +\newenvironment{quote} + {\list{}{\rightmargin\leftmargin}% + \item\relax} + {\endlist} +\newcommand\appendix{\par\small + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \renewcommand\thesection{\@Alph\c@section}} +\setlength\arraycolsep{1.5\p@} +\setlength\tabcolsep{6\p@} +\setlength\arrayrulewidth{.4\p@} +\setlength\doublerulesep{2\p@} +\setlength\tabbingsep{\labelsep} +\skip\@mpfootins = \skip\footins +\setlength\fboxsep{3\p@} +\setlength\fboxrule{.4\p@} +\renewcommand\theequation{\@arabic\c@equation} +\newcounter{figure} +\renewcommand\thefigure{\@arabic\c@figure} +\def\fps@figure{tbp} +\def\ftype@figure{1} +\def\ext@figure{lof} +\def\fnum@figure{\figurename~\thefigure} +\newenvironment{figure} + {\@float{figure}} + {\end@float} +\newenvironment{figure*} + {\@dblfloat{figure}} + {\end@dblfloat} +\newcounter{table} +\renewcommand\thetable{\@arabic\c@table} +\def\fps@table{tbp} +\def\ftype@table{2} +\def\ext@table{lot} +\def\fnum@table{\tablename~\thetable} +\newenvironment{table} + {\@float{table}} + {\end@float} +\newenvironment{table*} + {\@dblfloat{table}} + {\end@dblfloat} +% +\def \@floatboxreset {% + \reset@font + \small + \@setnobreak + \@setminipage +} +% +\newcommand{\tableheadseprule}{\noalign{\hrule height.375mm}} +% +\newlength\abovecaptionskip +\newlength\belowcaptionskip +\setlength\abovecaptionskip{10\p@} +\setlength\belowcaptionskip{0\p@} +\newcommand\leftlegendglue{} + +\def\fig@type{figure} + +\newdimen\figcapgap\figcapgap=3pt +\newdimen\tabcapgap\tabcapgap=5.5pt + +\@ifundefined{floatlegendstyle}{\def\floatlegendstyle{\bfseries}}{} + +\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\begingroup + \@parboxrestore + \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +\def\capstrut{\vrule\@width\z@\@height\topskip} + +\@ifundefined{captionstyle}{\def\captionstyle{\normalfont\small}}{} + +\long\def\@makecaption#1#2{% + \captionstyle + \ifx\@captype\fig@type + \vskip\figcapgap + \fi + \setbox\@tempboxa\hbox{{\floatlegendstyle #1\floatcounterend}% + \capstrut #2}% + \ifdim \wd\@tempboxa >\hsize + {\floatlegendstyle #1\floatcounterend}\capstrut #2\par + \else + \hbox to\hsize{\leftlegendglue\unhbox\@tempboxa\hfil}% + \fi + \ifx\@captype\fig@type\else + \vskip\tabcapgap + \fi} + +\newdimen\figgap\figgap=1cc +\long\def\@makesidecaption#1#2{% + \parbox[b]{\@tempdimb}{\captionstyle{\floatlegendstyle + #1\floatcounterend}#2}} +\def\sidecaption#1\caption{% +\setbox\@tempboxa=\hbox{#1\unskip}% +\if@twocolumn + \ifdim\hsize<\textwidth\else + \ifdim\wd\@tempboxa<\columnwidth + \typeout{Double column float fits into single column - + ^^Jyou'd better switch the environment. }% + \fi + \fi +\fi +\@tempdimb=\hsize +\advance\@tempdimb by-\figgap +\advance\@tempdimb by-\wd\@tempboxa +\ifdim\@tempdimb<3cm + \typeout{\string\sidecaption: No sufficient room for the legend; + using normal \string\caption. }% + \unhbox\@tempboxa + \let\@capcommand=\@caption +\else + \let\@capcommand=\@sidecaption + \leavevmode + \unhbox\@tempboxa + \hfill +\fi +\refstepcounter\@captype +\@dblarg{\@capcommand\@captype}} + +\long\def\@sidecaption#1[#2]#3{\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\begingroup + \@parboxrestore + \@makesidecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +% Define `acknowledgement' environment +\def\acknowledgement{\par\addvspace{17pt}\small\rmfamily +\trivlist\if!\ackname!\item[]\else +\item[\hskip\labelsep +{\bfseries\ackname}]\fi} +\def\endacknowledgement{\endtrivlist\addvspace{6pt}} +\newenvironment{acknowledgements}{\begin{acknowledgement}} +{\end{acknowledgement}} +% Define `noteadd' environment +\def\noteadd{\par\addvspace{17pt}\small\rmfamily +\trivlist\item[\hskip\labelsep +{\itshape\noteaddname}]} +\def\endnoteadd{\endtrivlist\addvspace{6pt}} + +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} +\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} +\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} +\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal} +\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal} +\newcommand\@pnumwidth{1.55em} +\newcommand\@tocrmarg{2.55em} +\newcommand\@dotsep{4.5} +\setcounter{tocdepth}{1} +\newcommand\tableofcontents{% + \section*{\contentsname}% + \@starttoc{toc}% + \addtocontents{toc}{\begingroup\protect\small}% + \AtEndDocument{\addtocontents{toc}{\endgroup}}% + } +\newcommand*\l@part[2]{% + \ifnum \c@tocdepth >-2\relax + \addpenalty\@secpenalty + \addvspace{2.25em \@plus\p@}% + \begingroup + \setlength\@tempdima{3em}% + \parindent \z@ \rightskip \@pnumwidth + \parfillskip -\@pnumwidth + {\leavevmode + \large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par + \nobreak + \if@compatibility + \global\@nobreaktrue + \everypar{\global\@nobreakfalse\everypar{}}% + \fi + \endgroup + \fi} +\newcommand*\l@section{\@dottedtocline{1}{0pt}{1.5em}} +\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} +\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} +\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} +\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}} +\newcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\listfigurename}% + {\listfigurename}}% + \@starttoc{lof}% + } +\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}} +\newcommand\listoftables{% + \section*{\listtablename + \@mkboth{\listtablename}{\listtablename}}% + \@starttoc{lot}% + } +\let\l@table\l@figure +\newdimen\bibindent +\setlength\bibindent{\parindent} +\def\@biblabel#1{#1.} +\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw + {\let\protect\noexpand + \immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} +\newenvironment{thebibliography}[1] + {\section*{\refname + \@mkboth{\refname}{\refname}}\small + \list{\@biblabel{\@arabic\c@enumiv}}% + {\settowidth\labelwidth{\@biblabel{#1}}% + \leftmargin\labelwidth + \advance\leftmargin\labelsep + \@openbib@code + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{\@arabic\c@enumiv}}% + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} +% +\newcount\@tempcntc +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@ifundefined + {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries + ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% + {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}% + \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne + \@citea\def\@citea{,\hskip0.1em\ignorespaces}\hbox{\csname b@\@citeb\endcsname}% + \else + \advance\@tempcntb\@ne + \ifnum\@tempcntb=\@tempcntc + \else\advance\@tempcntb\m@ne\@citeo + \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}} +\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else + \@citea\def\@citea{,\hskip0.1em\ignorespaces}% + \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else + {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi + \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi} +% +\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em} +\let\@openbib@code\@empty +\newenvironment{theindex} + {\if@twocolumn + \@restonecolfalse + \else + \@restonecoltrue + \fi + \columnseprule \z@ + \columnsep 35\p@ + \twocolumn[\section*{\indexname}]% + \@mkboth{\indexname}{\indexname}% + \thispagestyle{plain}\parindent\z@ + \parskip\z@ \@plus .3\p@\relax + \let\item\@idxitem} + {\if@restonecol\onecolumn\else\clearpage\fi} +\newcommand\@idxitem{\par\hangindent 40\p@} +\newcommand\subitem{\@idxitem \hspace*{20\p@}} +\newcommand\subsubitem{\@idxitem \hspace*{30\p@}} +\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax} + +\if@twocolumn + \renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width\columnwidth + \kern2.6\p@} +\else + \renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width.382\columnwidth + \kern2.6\p@} +\fi +\newcommand\@makefntext[1]{% + \noindent + \hb@xt@\bibindent{\hss\@makefnmark\enspace}#1} +% +\def\trans@english{\switcht@albion} +\def\trans@french{\switcht@francais} +\def\trans@german{\switcht@deutsch} +\newenvironment{translation}[1]{\if!#1!\else +\@ifundefined{selectlanguage}{\csname trans@#1\endcsname}{\selectlanguage{#1}}% +\fi}{} +% languages +% English section +\def\switcht@albion{%\typeout{English spoken.}% + \def\abstractname{Abstract}% + \def\ackname{Acknowledgements}% + \def\andname{and}% + \def\lastandname{, and}% + \def\appendixname{Appendix}% + \def\chaptername{Chapter}% + \def\claimname{Claim}% + \def\conjecturename{Conjecture}% + \def\contentsname{Contents}% + \def\corollaryname{Corollary}% + \def\definitionname{Definition}% + \def\emailname{E-mail}% + \def\examplename{Example}% + \def\exercisename{Exercise}% + \def\figurename{Fig.}% + \def\keywordname{{\bfseries Keywords}}% + \def\indexname{Index}% + \def\lemmaname{Lemma}% + \def\contriblistname{List of Contributors}% + \def\listfigurename{List of Figures}% + \def\listtablename{List of Tables}% + \def\mailname{{\itshape Correspondence to\/}:}% + \def\noteaddname{Note added in proof}% + \def\notename{Note}% + \def\partname{Part}% + \def\problemname{Problem}% + \def\proofname{Proof}% + \def\propertyname{Property}% + \def\questionname{Question}% + \def\refname{References}% + \def\remarkname{Remark}% + \def\seename{see}% + \def\solutionname{Solution}% + \def\tablename{Table}% + \def\theoremname{Theorem}% +}\switcht@albion % make English default +% +% French section +\def\switcht@francais{\svlanginfo +%\typeout{On parle francais.}% + \def\abstractname{R\'esum\'e\runinend}% + \def\ackname{Remerciements\runinend}% + \def\andname{et}% + \def\lastandname{ et}% + \def\appendixname{Appendice}% + \def\chaptername{Chapitre}% + \def\claimname{Pr\'etention}% + \def\conjecturename{Hypoth\`ese}% + \def\contentsname{Table des mati\`eres}% + \def\corollaryname{Corollaire}% + \def\definitionname{D\'efinition}% + \def\emailname{E-mail}% + \def\examplename{Exemple}% + \def\exercisename{Exercice}% + \def\figurename{Fig.}% + \def\keywordname{{\bfseries Mots-cl\'e\runinend}}% + \def\indexname{Index}% + \def\lemmaname{Lemme}% + \def\contriblistname{Liste des contributeurs}% + \def\listfigurename{Liste des figures}% + \def\listtablename{Liste des tables}% + \def\mailname{{\itshape Correspondence to\/}:}% + \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}% + \def\notename{Remarque}% + \def\partname{Partie}% + \def\problemname{Probl\`eme}% + \def\proofname{Preuve}% + \def\propertyname{Caract\'eristique}% +%\def\propositionname{Proposition}% + \def\questionname{Question}% + \def\refname{Bibliographie}% + \def\remarkname{Remarque}% + \def\seename{voyez}% + \def\solutionname{Solution}% +%\def\subclassname{{\it Subject Classifications\/}:}% + \def\tablename{Tableau}% + \def\theoremname{Th\'eor\`eme}% +} +% +% German section +\def\switcht@deutsch{\svlanginfo +%\typeout{Man spricht deutsch.}% + \def\abstractname{Zusammenfassung\runinend}% + \def\ackname{Danksagung\runinend}% + \def\andname{und}% + \def\lastandname{ und}% + \def\appendixname{Anhang}% + \def\chaptername{Kapitel}% + \def\claimname{Behauptung}% + \def\conjecturename{Hypothese}% + \def\contentsname{Inhaltsverzeichnis}% + \def\corollaryname{Korollar}% +%\def\definitionname{Definition}% + \def\emailname{E-Mail}% + \def\examplename{Beispiel}% + \def\exercisename{\"Ubung}% + \def\figurename{Abb.}% + \def\keywordname{{\bfseries Schl\"usselw\"orter\runinend}}% + \def\indexname{Index}% +%\def\lemmaname{Lemma}% + \def\contriblistname{Mitarbeiter}% + \def\listfigurename{Abbildungsverzeichnis}% + \def\listtablename{Tabellenverzeichnis}% + \def\mailname{{\itshape Correspondence to\/}:}% + \def\noteaddname{Nachtrag}% + \def\notename{Anmerkung}% + \def\partname{Teil}% +%\def\problemname{Problem}% + \def\proofname{Beweis}% + \def\propertyname{Eigenschaft}% +%\def\propositionname{Proposition}% + \def\questionname{Frage}% + \def\refname{Literatur}% + \def\remarkname{Anmerkung}% + \def\seename{siehe}% + \def\solutionname{L\"osung}% +%\def\subclassname{{\it Subject Classifications\/}:}% + \def\tablename{Tabelle}% +%\def\theoremname{Theorem}% +} +\newcommand\today{} +\edef\today{\ifcase\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space\number\day, \number\year} +\setlength\columnsep{1.5cc} +\setlength\columnseprule{0\p@} +% +\frenchspacing +\clubpenalty=10000 +\widowpenalty=10000 +\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil +\global\let\@textbottom\relax}} +\pagestyle{headings} +\pagenumbering{arabic} +\if@twocolumn + \twocolumn +\fi +\if@avier + \onecolumn + \setlength{\textwidth}{156mm} + \setlength{\textheight}{226mm} +\fi +\if@referee + \makereferee +\fi +\flushbottom +\endinput +%% +%% End of file `svjour2.cls'. diff --git a/vldb/pt/vldb.tex b/vldb/pt/vldb.tex new file mode 100644 index 0000000..807080a --- /dev/null +++ b/vldb/pt/vldb.tex @@ -0,0 +1,150 @@ +%%%%%%%%%%%%%%%%%%%%%%% 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}