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