%%%%%%%%%%%%%%%%%%%%%%% 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{epsfig}
\usepackage{textcomp}
\usepackage[latin1]{inputenc}
\usepackage{amssymb}

\DeclareGraphicsExtensions{.png} 
%
% \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{Space and Time Efficient Minimal Perfect Hash \\[0.2cm]
Functions for Very Large Databases\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}
We propose a novel external memory based algorithm for constructing minimal
perfect hash functions~$h$ for huge sets of keys.
For a set of~$n$ keys, our algorithm outputs~$h$ in time~$O(n)$.
The algorithm needs a small vector of one byte entries
in main memory to construct $h$.
The evaluation of~$h(x)$ requires three memory accesses for any key~$x$.
The description of~$h$ takes a constant number of bits
for each key, which is optimal, i.e., the theoretical lower bound is $1/\ln 2$
bits per key.
In our experiments, we used a collection of 1 billion URLs collected
from the web, each URL 64 characters long on average.
For this collection, our algorithm
(i) finds a minimal perfect hash function in approximately
3 hours using a commodity PC,
(ii) needs just 5.45 megabytes of internal memory to generate $h$
and (iii) takes 8.1 bits per key for the description of~$h$.
\keywords{Minimal Perfect Hashing \and Large Databases}
\end{abstract}

% main text

\def\cG{{\mathcal G}}
\def\crit{{\rm crit}}
\def\ncrit{{\rm ncrit}}
\def\scrit{{\rm scrit}}
\def\bedges{{\rm bedges}}
\def\ZZ{{\mathbb Z}}
\def\BSmax{\mathit{BS}_{\mathit{max}}}
\def\Bi{\mathop{\rm Bi}\nolimits}

\input{introduction}
%\input{terminology}
\input{relatedwork}
\input{thealgorithm}
\input{partitioningthekeys}
\input{searching}
%\input{computingoffset}
%\input{hashingbuckets}
\input{determiningb}
%\input{analyticalandexperimentalresults}
\input{analyticalresults}
%\input{results}
\input{conclusions}




%\input{acknowledgments}
%\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}
\input{appendix}
\end{document}