103 lines
3.3 KiB
TeX
103 lines
3.3 KiB
TeX
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\documentclass[11pt,a4paper]{scrartcl}
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\usepackage[ngerman]{babel} % Deutsches Wörterbuch usw.
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\usepackage[T1]{fontenc}
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\usepackage[utf8]{inputenc}
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\usepackage{times} % Skalierbarer und lesbarer Zeichensatz
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage[usenames,dvipsnames]{xcolor}
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\inputencoding{utf8} % Wir wollen UTF8(=keine Probleme mit Umlauten etc.)
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\parindent0em % Keine amerikanische Einrückung am Anfang von Paragraphen
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\usepackage[lmargin=2cm,rmargin=3.5cm,tmargin=2cm,bmargin=2cm]{geometry}
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\parindent0em
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\usepackage{fancyhdr}
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\pagestyle{fancy}
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%opening
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\fancyhf{}
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\fancyhead[L]{\textbf{Message Passing Programming\\Parallele Algorithmen und Datenverarbeitung}}
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\fancyhead[R]{\textbf{Stefan Dresselhaus\\Thomas Pajenkamp}}
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\fancyfoot[C]{\thepage}
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\fancyfoot[R]{24. November 2013}
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\usepackage{algorithm}
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\usepackage[noend]{algpseudocode}
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\newcommand{\abs}[1]{\ensuremath{\left\lvert#1\right\rvert}}
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\newcommand{\norm}[1]{\ensuremath{\left\lVert#1\right\rVert}}
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\newcommand{\mean}[1]{\ensuremath{\overline{#1}}}
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\newcommand{\transp}[1]{\ensuremath{#1^{\mathsf{T}}}}
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% Ende der Voreinstellungen
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\begin{document}
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%\title{Message Passing Programming}
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%\author{Stefan Dresselhaus \and Thomas Pajenkamp}
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%\date{24. November 2013}
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%\maketitle
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\section*{Heuristik für \glqq{}Densely-connected Biclustering\grqq{}}
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\begin{algorithm*}
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\caption{Densely-connected Biclustering}
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\begin{algorithmic}[1]
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\Function{testHomogenity}{$A$, $\omega$, $\delta$, $g$}
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\State $l \gets (\transp{A})_{g_0}$, $l \gets u$
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\ForAll {nodes $i$ from $g \setminus \lbrace g_0\rbrace$}
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\ForAll {dimensions $d$ of attribute matrix $A$}
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\State $l \gets \min\lbrace l_d, A_{id}\rbrace$, $u \gets \max\lbrace l_d, A_{id}\rbrace$
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\EndFor
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\EndFor
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\State $c \gets 0$
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\ForAll {dimensions $d$ of attribute matrix $A$}
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\If {$\abs{u_d - l_d} \leq \omega_d $}
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\State $c \gets c+1$
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\If {$c \geq \delta$}
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\State \Return {true}
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\EndIf
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\EndIf
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\EndFor
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\Return {false}
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\EndFunction
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\end{algorithmic}
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\begin{algorithmic}[1]
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\Function{preprocessGraph}{$M$, $A$, $\omega$, $\delta$}
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\State $G \gets \emptyset$
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\ForAll {rows $i$ of adjascency matrix $M$}
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\ForAll {columns $j$ of adjascency matrix $M$}
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\If {$M_{ij} = 1$}
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\If {\Call{testHomogenity}{$A$, $\omega$, $\delta$, $\lbrace i , j\rbrace$}}
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\State $G \gets G \cup \lbrace \lbrace i, j\rbrace \rbrace$
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\Else
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\State $M_{ij} = 0$, $M_{ji} = 0$
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\EndIf
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\EndIf
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\EndFor
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\EndFor
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\Return {$G$}
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\EndFunction
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\end{algorithmic}
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\begin{algorithmic}[1]
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\Function{DCB}{$M$, $A$, $\alpha$, $\omega$, $\delta$}
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\State $G \gets $ \Call{preprocessGraph}{$M$, $A$, $\omega$, $\delta$}
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\State $F \gets \emptyset$
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\While {$G \neq \emptyset$}
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\State $G' \gets G$, $G \gets \emptyset$
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\ForAll {node sets $g$ in $G'$}
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\State $b \gets \text{true}$
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\ForAll {connected nodes $h$ with $h > \max g$}
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\State $\hat{g} \gets g \cup \lbrace h\rbrace$
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\If {\Call{testHomogenity}{$A$, $\omega$, $\delta$, $\hat{g}$} $\wedge$ \Call{graphDensity}{$M$, $\hat{g}$} $\leq$ $\alpha$}
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\State $G \gets G \cup \lbrace \hat{g} \rbrace$
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\State $b \gets \text{false}$
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\EndIf
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\EndFor
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\If {$b$}
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\State $F \gets F \cup \lbrace g\rbrace$
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\EndIf
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\EndFor
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\EndWhile
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\EndFunction
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\end{algorithmic}
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\end{algorithm*}
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\end{document}
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