diff --git a/.gitignore b/.gitignore index ab49a73..cc46af2 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,4 @@ -talk.pdf +upperbounds.pdf # Created by https://www.gitignore.io/api/latex,tex,emacs,linux diff --git a/inputs/elimination.tex b/inputs/elimination.tex new file mode 100644 index 0000000..ad333eb --- /dev/null +++ b/inputs/elimination.tex @@ -0,0 +1,20 @@ +\begin{frame}{Table of contents} + \setbeamertemplate{section in toc}[sections numbered] + \setbeamertemplate{subsection in toc}[square] + \tableofcontents[sections={2}] +\end{frame} + + +\subsection{Idea} + +\begin{frame}{} + +\end{frame} + +\subsection{Test1} +\subsection{Test2} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../upperbounds" +%%% End: diff --git a/inputs/introduction.tex b/inputs/introduction.tex new file mode 100644 index 0000000..603268b --- /dev/null +++ b/inputs/introduction.tex @@ -0,0 +1,14 @@ +\begin{frame}{Table of contents} + \setbeamertemplate{section in toc}[sections numbered] + \tableofcontents[hideallsubsections] +\end{frame} + +\section{Introduction} + + + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../upperbounds" +%%% End: diff --git a/inputs/motivation.tex b/inputs/motivation.tex new file mode 100644 index 0000000..0437595 --- /dev/null +++ b/inputs/motivation.tex @@ -0,0 +1,106 @@ +\begin{frame}{General Motivation} + \begin{columns}[c] + \begin{column}{0.5\textwidth} + \begin{enumerate} + \item Choose infeasible problem + \begin{itemize} + \item Combinatorial Problems + \item Computational Biology + \item Constraint Satisfaction + \item \dots{} + \end{itemize} + \item Find FPT$_{tw}$ algorithm + \item Model problem as graph + \item Compute \emph{tree composition} with small \emph{tree width} + \uncover<2>{\alert{\item Tract the intractable}} + \end{enumerate} + \end{column} + + \begin{column}{0.8\textwidth} + \begin{center} + \begin{tikzpicture}[xscale=1.5,yscale=1.6] + \tikzstyle{every node}=[] + \tikzstyle{every path}=[line width=0pt] + % + \begin{scope} + \draw[fill,green,opacity=1,line width=0] + (-1.5,0) -- (1.5,0) + (-1,0) .. controls (-.8,1) and (.8,1) .. (1,0); + ; + % + \draw[fill,green!50,opacity=1,line width=0] + (-1,0) .. controls (-.8,1) and (.8,1) .. (1,0) + (1.1,0) .. controls (1.1,2.5) and (-1.1,2.5) .. (-1.1,0) + ; + % + \draw[fill,red!50,opacity=1,line width=0] + (1.1,0) .. controls (1.1,2.5) and (-1.1,2.5) .. (-1.1,0) + (-1.2,0) .. controls (-1.2,3.5) and (1.2,3.5) .. (1.2,0) + ; + % + \draw[fill,red!100,opacity=1,line width=0] + (-1.2,0) .. controls (-1.2,3.5) and (1.2,3.5) .. (1.2,0) + (1.5,0) .. controls (1.5,4.5) and (-3,4.5) .. (-1.5,0) + ; + \draw[fill,red!100,opacity=1,line width=0] + (-1.2,0) .. controls (-1.2,3.5) and (1.2,3.5) .. (1.2,0) + (1.5,0) .. controls (3,4.5) and (-1.5,4.5) .. (-1.5,0) + ; + % + \draw + (-1.5,0) -- (1.5,0) + (0,0.25) node[] {P} + (-1,0) .. controls (-.8,1) and (.8,1) .. (1,0) + % + (0,1.25) node[] {FPT} + (-1.1,0) .. controls (-1.1,2.5) and (1.1,2.5) .. (1.1,0) + % + (0,2.15) node[] {W[i]} + (-1.2,0) .. controls (-1.2,3.5) and (1.2,3.5) .. (1.2,0) + % + (-1,2.9) node[] {XP} + % (0,2.8) node[circle,black,fill,inner sep=0pt] {} + % (0,2.6) node[circle,black,fill,inner sep=0pt] {} + % (0,2.4) node[circle,black,fill,inner sep=0pt] {} + (-1.5,0) .. controls (-3,4.5) and (1.5,4.5) .. (1.5,0) + % + (1,2.9) node[] {paraNP} + % (0,2.8) node[circle,black,fill,inner sep=0pt] {} + % (0,2.6) node[circle,black,fill,inner sep=0pt] {} + % (0,2.4) node[circle,black,fill,inner sep=0pt] {} + (-1.5,0) .. controls (-1.5,4.5) and (3,4.5) .. (1.5,0) + ; + \end{scope} + \end{tikzpicture} + \end{center} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Why Upper Bounds?} + + \metroset{block=fill} + + \begin{block}{We want (efficiently)} + \begin{itemize} + \item \emph{High} Lower Bound: Tree dec. not the right tool + \item \emph{Low} Upper Bound: Tree dec. works + \item Other combinations? -- Not so useful + \end{itemize} + \end{block} + + \begin{block}{What this paper is about} + \smallskip + Exact algorithm: Huge constant factor \cite{roehrig1998} + \begin{itemize} + \item[$\rightarrow$] Find a non-optimal tree decomposition + \item[$\rightarrow$] This is also an Upper Bound + \end{itemize} + \end{block} + +\end{frame} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "../upperbounds" +%%% End: diff --git a/res/down.png b/res/down.png new file mode 100644 index 0000000..3f82960 Binary files /dev/null and b/res/down.png differ diff --git a/res/up.png b/res/up.png new file mode 100644 index 0000000..2331a3e Binary files /dev/null and b/res/up.png differ diff --git a/talk.tex b/talk.tex deleted file mode 100644 index aa7e649..0000000 --- a/talk.tex +++ /dev/null @@ -1,25 +0,0 @@ -\documentclass{beamer} -\usepackage[english]{babel} -\usepackage[utf8]{inputenc} -\usepackage{graphicx} -\usepackage[T1]{fontenc} -%\usepackage{lmodern} -%\usepackage{helvet} - -\usetheme{metropolis} - -\subject{Upper Bounds} -\title[Upper Bounds]{Upper Bounds for Treewidth} -\subtitle{} -\author{Armin Friedl} -\date{\today} - -\begin{document} -\frame{\titlepage} - -\end{document} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: t -%%% End: diff --git a/upperbounds.bib b/upperbounds.bib new file mode 100644 index 0000000..f4c1b16 --- /dev/null +++ b/upperbounds.bib @@ -0,0 +1,32 @@ +% This file was created with JabRef 2.10. +% Encoding: ISO8859_1 + + +@Article{bodlaender2010, + Title = {Treewidth computations I. Upper bounds}, + Author = {Hans L. Bodlaender and Arie M.C.A. Koster}, + Year = {2010}, + Doi = {http://dx.doi.org/10.1016/j.ic.2009.03.008}, + ISSN = {0890-5401}, + Number = {3}, + Pages = {259 - 275}, + Url = {http://www.sciencedirect.com/science/article/pii/S0890540109000947}, + Volume = {208}, + + Abstract = {For more and more applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast. This paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining the treewidth of a graph and finding tree decompositions. Each of the heuristics produces tree decompositions whose width may be larger than the optimal width. However, experiments show that in many cases, the heuristics give tree decompositions whose width is close to the exact treewidth of the input graphs.}, + Journal = {Information and Computation}, + Keywords = {Treewidth} +} + +@Mastersthesis{roehrig1998, + Title = {{{Tree Decomposition: A Feasibility Study}}}, + Author = {Hein R{\"o}hrig}, + Institution = {Max-Planck-Institut für Informatik}, + Year = {1998}, + Location = {Saarbrücken, Germany}, + Url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.132.7594&rep=rep1&type=pdf}, + + Owner = {armin}, + Timestamp = {2016.06.26} +} + diff --git a/upperbounds.pdf b/upperbounds.pdf new file mode 100644 index 0000000..910de16 Binary files /dev/null and b/upperbounds.pdf differ diff --git a/upperbounds.tex b/upperbounds.tex new file mode 100644 index 0000000..7024dcb --- /dev/null +++ b/upperbounds.tex @@ -0,0 +1,65 @@ +\documentclass[10pt]{beamer} +\usepackage{appendixnumberbeamer} +\usepackage{booktabs} +\usepackage[scale=2]{ccicons} +\usepackage{pgfplots} +\usepgfplotslibrary{dateplot} +\usepackage{xspace} +%\usepackage{graphicx} +\usepackage{scalerel} + +% == General Beamer Settings == +\usetheme{metropolis} + +% == Presentation Settings == +\def\thumbsup{\scalerel*{\includegraphics{res/up.png}}{O}} +\def\thumbsdown{\scalerel*{\includegraphics{res/down.png}}{O}} + +\subject{Upper Bounds} +\title[Upper Bounds]{Treewidth computations I. Upper bounds} +\subtitle{Hans L. Bodlaender, Arie M.C.A Koster} +\author{Armin Friedl} +\date{\today} + +\begin{document} +\maketitle + +\begin{frame}{Table of contents} + \setbeamertemplate{section in toc}[sections numbered] + \tableofcontents[hideallsubsections] +\end{frame} + +\section{Motivation} +\input{inputs/motivation} + +\section{Elimination Ordering Methods} +\input{inputs/elimination} + +\begin{frame}{Table of contents} + \setbeamertemplate{section in toc}[sections numbered] + \setbeamertemplate{subsection in toc}[square] + \tableofcontents[sections={2}] +\end{frame} + +\subsection{Idea} + + +\subsection{Test1} +\subsection{Test2} + +\section{Separator Methods} + +\section{Results} + +\begin{frame}[allowframebreaks]{References} + \nocite{bodlaender2010} + \bibliography{upperbounds} + \bibliographystyle{abbrv} +\end{frame} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: