From: Martin Mares Date: Sat, 13 Sep 2008 14:37:34 +0000 (+0200) Subject: Removed the Preface. X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=04160c5697523391029cd65c0889b476eefa28e4;p=saga.git Removed the Preface. --- diff --git a/Makefile b/Makefile index 7f3bb11..eed7aac 100644 --- a/Makefile +++ b/Makefile @@ -1,6 +1,6 @@ all: saga.ps -CHAPTERS=pref mst ram adv opt dyn appl epilog notation +CHAPTERS=mst ram adv opt dyn appl epilog notation %.dvi: %.tex macros.tex fonts12.tex fonts10.tex biblio.bib mjalpha.bst tex $< && mv $*.toc $*.tok diff --git a/mst.tex b/mst.tex index d4bf952..97dad84 100644 --- a/mst.tex +++ b/mst.tex @@ -54,6 +54,25 @@ various approaches to the problem including randomization and solving of importa special cases. At several places, we will try to contribute our little stones to this mosaic. +When compared with the earlier surveys on the minimum spanning trees, most +notably Graham and Hell \cite{graham:msthistory} and Eisner \cite{eisner:tutorial}, +this work adds many of the recent advances, the dynamic algorithms and +also the relationship with computational models. + +\nota +We have tried to stick to the usual notation except where it was too inconvenient. +Most symbols are defined at the place where they are used for the first time. +A~complete index of symbols with pointers to their definitions is then available +in Appendix~\ref{notapp}. This appendix also describes the formalism of +multigraphs and of the Ackermann's function, both of which are not defined +consistently in the common literature. + +To avoid piling up too many symbols at places that speak about a~single fixed graph, +this graph is always called~$G$, its set of vertices and edges are denoted by $V$ +and~$E$ respectively, and I~also use~$n$ for the number of its vertices and $m$~for +the number of edges. At places where there could be a~danger of confusion, more explicit notation +is used instead. + %-------------------------------------------------------------------------------- \section{Basic properties}\id{mstbasics}% diff --git a/pref.tex b/pref.tex deleted file mode 100644 index c06716c..0000000 --- a/pref.tex +++ /dev/null @@ -1,103 +0,0 @@ -\ifx\endpart\undefined -\input macros.tex -\fi - -\unchapter{Preface} - -This thesis tells the story of two well-established problems of algorithmic -graph theory: the minimum spanning trees and ranks of permutations. At distance, -both problems seem to be simple, boring and already solved, because we have poly\-nom\-ial-time -algorithms for them since ages. But when we come closer and seek algorithms that -are really efficient, the problems twirl and twist and withstand many a~brave -attempt at the optimum solution. They also reveal a~vast and diverse landscape -of a~deep and beautiful theory. Still closer, this landscape turns out to be interwoven -with the intricate details of various models of computation and even of arithmetics -itself. - -I have tried to cover all known important results on both problems and unite them -in a~single coherent theory. At many places, I have attempted to contribute my own -little stones to this mosaic: several new results, simplifications of existing -ones, and last, but not least filling in important details where the original -authors have missed some. - -When compared with the earlier surveys on the minimum spanning trees, most -notably Graham and Hell \cite{graham:msthistory} and Eisner \cite{eisner:tutorial}, -this work adds many of the recent advances, the dynamic algorithms and -also the relationship with computational models. No previous work covering -the ranking problems in their entirety is known. - -The early parts of this thesis also served as a~basis for a~course on graph -algorithms which I was teaching at our faculty during years 2006 and~2007. They are -included in the textbook \cite{mm:ga} which I have written for this course. - -\def\ss#1{\medskip\>{\bo #1}\enspace\eatspaces} - -\ss{My original results} - -\itemize\ibull -\:The lower bound in Section \ref{contalg}. Not published yet. -\:The tree isomorphism algorithm in Section \ref{bucketsort}. Not published yet. -\:One of the algorithms for minor-closed graph classes in Section \ref{minorclosed}. Published in \cite{mm:mst}. -\:The linear-time verification algorithm in Section \ref{verifysect} is a~simplification - of the algorithm of King \cite{king:verifytwo} and it corrects many omissions - in the original paper. Not published yet. -\:The ranking algorithms in Sections \ref{ranksect} to \ref{kpranksect} are results of joint research with Milan Straka. - Published in \cite{mm:rank}. -\:The remaining sections of Chapter \ref{rankchap} contain unpublished original results. -\endlist - -\ss{Other minor contributions} - -\itemize\ibull -\:The flattening procedure in Section \ref{bucketsort}. Included in \cite{mm:mst}. -\:The unified view of vector computations in Section \ref{bitsect}. Published - in the textbook \cite{mm:ga}. The main ideas of this section were also included - in the yearbook of the Czech Mathematical Olympiad \cite{horak:mofivefour}. -\:Slight simplifications of the soft heaps and their analysis in Section \ref{shsect}. -\:The dynamic MST algorithm for graphs with limited edge weights in Section \ref{dynmstsect}. -\endlist - -\vfill\eject - -\ss{Acknowledgements} - -First of all, I~would like to thank my supervisor, Jaroslav Ne\v{s}et\v{r}il, for -introducing me to the world of discrete mathematics and gently guiding my attempts -to explore it with his deep insight. I~am very grateful to all members of the -Department of Applied Mathematics and the Institute for Theoretical Computer -Science for the work environment which was friendly and highly inspiring. -I~cannot forget the participants of the department's seminars, -who have listened to my talks and provided lots of important feedback. -I~also send my acknowledgements to the members of the Math department at ETH Z\"urich and of DIMACS -at the Rutgers University (especially to J\'anos Koml\'os) where I~spent several -pleasant months working on what finally become a~part of this thesis. - -I~also thank to my family for supporting me during the plentiful years of my study, -to my girlfriend Ani\v{c}ka for lots of patience when I~was caught up by my work and -hardly speaking at all, to all the polar bears of Kobylisy for their furry presence, and -finally to our cats Minuta and Dami\'an for their mastership in hiding my -papers, which has frequently forced me to think of new ways of looking at problems -when the old ones were impossible to find. - -\ss{Notation} - -I~have tried to stick to the usual notation except where it was too inconvenient. -Most symbols are defined at the place where they are used for the first time. -A~complete index of symbols with pointers to their definitions is then available -in Appendix~\ref{notapp}. This appendix also describes the formalism of -multigraphs and of the Ackermann's function, both of which are not defined -consistently in the common literature. - -To avoid piling up too many symbols at places that speak about a~single fixed graph, -this graph is always called~$G$, its set of vertices and edges are denoted by $V$ -and~$E$ respectively, and I~also use~$n$ for the number of its vertices and $m$~for -the number of edges. At places where there could be a~danger of confusion, more explicit notation -is used instead. - - -\bigskip - -So, my gentle reader, let us nestle deep in an~ancient wing armchair. The saga of the -graph algorithms begins~\dots - -\endpart diff --git a/saga.tex b/saga.tex index 8724eeb..59e3d70 100644 --- a/saga.tex +++ b/saga.tex @@ -2,8 +2,6 @@ \input fonts12.tex \let\endpart=\relax -\input pref.tex - \unchapter{Table of contents} \includetoc