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main.tex
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\documentclass[%
25pt, a1paper, portrait,%
blockverticalspace=15pt,%
colspace=15pt,%
margin=0pt,%
innermargin=20pt,%
]{tikzposter}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PACKAGES
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[english]{babel}
\usepackage{amsmath, amsthm, amssymb, latexsym}
\usepackage[utf8]{inputenc}
\usepackage{etoolbox}
\usepackage{xparse}
\usepackage{subcaption}
\usepackage{blindtext}
\usepackage{geometry}
\usepackage{calculator}
\usepackage[thicklines]{cancel}
\usepackage{diagbox}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage[absolute, overlay]{textpos}
\input{src/cmds/commons}
\input{src/cmds/commands}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TITLE
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{%
Path Planning with CPD Heuristics%
}
\author{Massimo Bono$^1$, Alfonso E. Gerevini$^1$, Daniel D. Harabor$^2$, Peter J. Stuckey$^2$}
\date{\today}
\institute{%
$^1$\setFontSize{42}{Dipartimento Di Ingegneria dell'Informazione, Università degli Studi di Brescia, Brescia, Italy}%
\\%
$^2$\setFontSize{42}{Faculty of Information Technology, Monash University, Melbourne, Australia}%
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% STYLE
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\definecolor{theColorThree}{rgb}{0.2, 0.2, 0.6}
\definecolorpalette{customColorPalette}{%
\definecolor{colorOne}{named}{theColorOne}%
\definecolor{colorTwo}{named}{theColorTwo}%
\definecolor{colorThree}{named}{theColorThree}
}
\usetheme{Autumn}
\usecolorstyle[colorPalette=customColorPalette]{Germany}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% configuration of tikzposter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%remove logo https://tex.stackexchange.com/a/263278/145331
\tikzposterlatexaffectionproofoff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TEXPOS CONFIGURATION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setlength{\TPHorizModule}{1mm}
\setlength{\TPVertModule}{1mm}
\dimendef\prevdepth=0
%\textblockorigin{0mm}{0mm} % start everything near the top-left corner
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TIKZ CONFIGURATION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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shape=circle,%
draw=blue!30,%
fill=blue!15,%
minimum size=10pt,%
line width=4pt,%
radius=1cm,%
inner sep=3pt,%
node distance=3.5cm,%
}}
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shape=circle,%
draw=blue!50,%
fill=blue!30,%
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draw=blue!50,%
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shape=circle,%
draw=yellow!80,%
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\NewDocumentCommand{\edgeLabel}{s m}{%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DOCUMENT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\maketitle
\begin{textblock}{45}[0.5, 0.5](55,30)
\includegraphics[width=45mm]{src/images/unibs-onlylogo3}
\end{textblock}
\begin{textblock}{45}[0.5, 0.5](539,30)
\includegraphics[width=45mm]{src/images/monash-onlylogo2}
\end{textblock}
\block{Abstract}{\normalsize{%
Compressed Path Databases (CPDs) are a leading technique for optimal pathfinding in graphs with static edge costs. In this work we investigate CPDs as admissible heuristic functions and we apply them in two distinct settings: problems where the graph is subject to dynamically changing costs, and anytime settings where deliberation time is limited. Conventional heuristics derive cost-to- go estimates by reasoning about a tentative and usually infeasible path, from the current node to the target. CPD-based heuristics derive cost-to-go estimates by computing a concrete and usually feasible path. We exploit such paths to bound the optimal solution, not just from below but also from above. We demonstrate the benefit of this approach in a range of experiments on standard gridmaps and in comparison to Landmarks, a popular alternative also developed for searching in explicit state-spaces.
}}
\begin{columns}
\column{0.37}{%
\block{Context}{%
\begin{itemize}
\item[\color{theColorOne}\Large{$\diamond$}] Path planning episodes are independent from each others;
\item[\color{theColorOne}\Large{$\diamond$}] fixed start and target locations;
\item[\color{theColorOne}\Large{$\diamond$}] original graph map known a priori;
\item[\color{theColorOne}\Large{$\diamond$}] distribution of edge costs changes (\textit{perturbations}) over map unkown a priori;
\item[\color{theColorOne}\Large{$\diamond$}] perturbations can \textbf{only increase} original edge cost;
\item[\color{theColorOne}\Large{$\diamond$}] perturbations detected at the beginning of each path planning episodes and then assumed fixed.
\end{itemize}
}
}
\column{0.63}{%
\block{Problem}{%
\begin{minipage}[b]{0.31\linewidth}%
\centering%
\textbf{Original map}%
\medskip\medskip\medskip
\input{src/tikzs/originalgraph.tikz}
\end{minipage}\hfill%
\begin{minipage}[b]{0.31\linewidth}
\centering
\textbf{Solution of query\\ $\mathbf{q = (s_{0,0}, s_{2,2})}$}
\medskip\medskip\medskip
\input{src/tikzs/originalgraphquery.tikz}
\end{minipage}\hfill%
\begin{minipage}[b]{0.31\linewidth}
\centering
\textbf{Problem: solution of $\mathbf{q}$ over map with \textit{perturbations}?}
\medskip\medskip\medskip
\input{src/tikzs/perturbatedgraphquery.tikz}
\end{minipage}%
}
}
\end{columns}
\block{\CPDSearch{} $\Rightarrow$ Exploit \CPDPathsName{} in an \A{} variant}{%
\begin{minipage}{0.26\textwidth}
\begin{tabular}{c|cccccccc}
\diagbox[height=15mm]{s}{t} & $s_{0,0}$ & $s_{0,1}$ & $s_{0,2}$ &$s_{1,0}$ &$s_{1,1}$ &$s_{1,2}$ &$s_{2,0}$ &$s_{2,2}$ \\ \hline
$s_{0,0}$ & * & a & a & e & a & a & e & a \\
$s_{0,1}$ & a & * & b & a & g & g & a & g \\
$s_{0,2}$ & b & b & * & b & b & h & b & h \\
$s_{1,0}$ & e & e & e & * & c & c & f & c \\
$s_{1,1}$ & g & g & g & c & * & d & c & d \\
$s_{1,2}$ & d & d & h & d & d & * & d & i \\
$s_{2,0}$ & f & f & f & f & f & f & * & f \\
$s_{2,2}$ & i & i & i & i & i & i & i & * \\
\end{tabular}
\end{minipage}\quad%
\begin{minipage}{0.23\textwidth}
\centering
\textbf{Admissible heuristic}
\medskip\medskip\medskip
\input{src/tikzs/admissibleheuristic.tikz}
\end{minipage}%
\begin{minipage}{0.23\textwidth}
\centering
\textbf{Early Termination}
\medskip\medskip\medskip
\input{src/tikzs/earlytermination.tikz}
\end{minipage}%
\begin{minipage}{0.23\textwidth}
\centering
\textbf{Obtain solution bounds}
\medskip\medskip\medskip
\input{src/tikzs/solutionbounds.tikz}
\end{minipage}
}
\begin{columns}
\column{0.63}{%
\block[bodyinnersep=5pt]{Optimal scenario}{%
\begin{minipage}{0.5\linewidth}
\centering
\includegraphics[width=1.0\linewidth]{src/images/maze512-1-4}
\end{minipage}\hfill%
\begin{minipage}{0.5\linewidth}
\centering
\includegraphics[width=1.0\linewidth]{src/images/hrt201n}
\end{minipage}
\medskip\medskip\medskip\medskip
\phantom{x}
}
}%
\column{0.37}{%
\block[bodyinnersep=5pt]{Anytime scenario}{%
\normalsize{In $100\mu$s: \anytimeCPDSearch{} has solutions for $>75\%$ of instances while (\AWA{}) has them for $<25\%$.}
\includegraphics[width=1.0\linewidth]{src/images/anytime}
}
}
\end{columns}
\end{document}