From cd4a8e81cd090b6c108261e9f759564ca66e807a Mon Sep 17 00:00:00 2001 From: Armin Friedl Date: Mon, 27 Jun 2016 00:30:37 +0200 Subject: [PATCH] motivation finished --- .gitignore | 2 +- inputs/elimination.tex | 20 ++++++++ inputs/introduction.tex | 14 ++++++ inputs/motivation.tex | 106 ++++++++++++++++++++++++++++++++++++++++ res/down.png | Bin 0 -> 2388 bytes res/up.png | Bin 0 -> 2472 bytes talk.tex | 25 ---------- upperbounds.bib | 32 ++++++++++++ upperbounds.pdf | Bin 0 -> 101399 bytes upperbounds.tex | 65 ++++++++++++++++++++++++ 10 files changed, 238 insertions(+), 26 deletions(-) create mode 100644 inputs/elimination.tex create mode 100644 inputs/introduction.tex create mode 100644 inputs/motivation.tex create mode 100644 res/down.png create mode 100644 res/up.png delete mode 100644 talk.tex create mode 100644 upperbounds.bib create mode 100644 upperbounds.pdf create mode 100644 upperbounds.tex 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 0000000000000000000000000000000000000000..3f82960413c13214e6c494c05f9e6fb1f04fe80d GIT binary patch literal 2388 zcmX9=dpy(o8~=WXxow2pujMoyYRx6nl1wIYo7$qHv#~6MxlB@rukGNtBqf(zYWP(% zxu2Mjq1=jcODdVYLO@4zaCC0K0$5RmipwPZ$U}q?o zCMLBa30{#WLj5BzQp3*yL~1}tB-)KYGKexq??;{zQ`Cx1-M9)Fatunc}NXNULU7ccc{WZ2hw% zk>ZCBf6vO9*pVxj(`Kb1(b-m1br_LE#b{V2f}Hg7 z8XCqRN+6l55ZYc}B{xub29D|v^a7nJN>_jtp(bDdo*;{XEL(z zMRe(CS<>&lzOZoxZM!4CBjdJXV9~MUEYJSqUNVXjm8RpIr$ za@SnJ{}|7RHs+4xTSHBWP}~A`X}@FL4C-Zy;@}Fg5_<`_^Zsfaza*Q1XeiEhYljB=q!soM6CQ08AA_6) zhrdw?nSe^G{>C5b1Q_E%bKI9_R2$IhgNRN{;D2~-Bsj#8V^DM50KK&F`CoHBNeXoy zFX2^%ZJ0tpXJyTp3-i{Pt_0E2WJtdK3Tz&1i8p?tO1A-Lowf=TJ3^DKOR#Li6iMNQ z0e4%~k15GJ!C5t;RD*A^6Ht*+Bp3eFJ`?DKjJs4-TwyK}aFLyQcDJOJ@)ZOnDAxtLjBoBrpqqhw zs3zvR{0kZ^Otsifev9kO773y>Q z^WHrTns<36o z4DqZTh*z;~HqGh1lo4`bZ~#0T9}A!BZP-8gsdj{1$26W@+gzDU@(&^|1mwwupMLF2 z3>^}6yq&UU^6D(y;S(0b&{v{WfNPn?Lcl^#eObL5(_SIHRE3lnPV~rV%?lQ&|9QIh zne9U#3mRs^V7awOYsQ_iEh(`6d>5t1qY6PXB#oAG-k2Dh?M{Oo*8M7s_`$?KB$H@W zicKiK-ulg;{oKUTluX-)9+9*veVxWSY#MwKWhuqK^;IWVQNK-H0H!-bBil@%weAMt zkny_2`s)VmP5-91$Am%I?Z?+;z0{s#8p6!dZd&vt1NWXQZRD<0{2m_>L7! 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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 0000000000000000000000000000000000000000..910de16513e0b71721075449d9249ba0def246b5 GIT binary patch literal 101399 zcmcG$1yChxvaXH0HQG2d?(XjH?(VX1XuN^Oy>WMUYuw$Xad&t3OYfOEapvFq{CCfd zdkLbbT2a&@SHAgtSy^vDA}=gT!$8XdLo)fRZvlpdnSh=EU}y=$%?(2*ZDMQYWKO`$ 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