104 lines
3.3 KiB
TeX
104 lines
3.3 KiB
TeX
\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 adjacency matrix $M$}
|
|
\ForAll {columns $j$ of adjacency 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
|
|
\State \Return $F$
|
|
\EndFunction
|
|
\end{algorithmic}
|
|
\end{algorithm*}
|
|
|
|
\end{document} |