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added Pseudocode example
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Martin Thoma
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3 changed files with 239 additions and 0 deletions
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\usepackage{tikz}
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\usetikzlibrary{calc}
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\usepackage{xcolor}
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\makeatletter
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% to change colors
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\newcommand{\fillcol}{green!20}
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\newcommand{\bordercol}{black}
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% code from Andrew Stacey (with small adjustment to the border color)
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% http://tex.stackexchange.com/questions/51582/background-coloring-with-overlay-specification-in-algorithm2e-beamer-package
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\newcounter{jumping}
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\resetcounteronoverlays{jumping}
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\def\jump@setbb#1#2#3{%
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\@ifundefined{jump@#1@maxbb}{%
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\expandafter\gdef\csname jump@#1@maxbb\endcsname{#3}%
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}{%
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\csname jump@#1@maxbb\endcsname
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\pgf@xa=\pgf@x
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\pgf@ya=\pgf@y
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#3
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\pgfmathsetlength\pgf@x{max(\pgf@x,\pgf@xa)}%
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\pgfmathsetlength\pgf@y{max(\pgf@y,\pgf@ya)}%
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\expandafter\xdef\csname jump@#1@maxbb\endcsname{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}%
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}
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\@ifundefined{jump@#1@minbb}{%
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\expandafter\gdef\csname jump@#1@minbb\endcsname{#2}%
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}{%
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\csname jump@#1@minbb\endcsname
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\pgf@xa=\pgf@x
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\pgf@ya=\pgf@y
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#2
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\pgfmathsetlength\pgf@x{min(\pgf@x,\pgf@xa)}%
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\pgfmathsetlength\pgf@y{min(\pgf@y,\pgf@ya)}%
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\expandafter\xdef\csname jump@#1@minbb\endcsname{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}%
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}
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}
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\tikzset{%
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remember picture with id/.style={%
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remember picture,
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overlay,
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draw=\bordercol,
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save picture id=#1,
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},
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save picture id/.code={%
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\edef\pgf@temp{#1}%
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\immediate\write\pgfutil@auxout{%
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\noexpand\savepointas{\pgf@temp}{\pgfpictureid}}%
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},
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if picture id/.code args={#1#2#3}{%
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\@ifundefined{save@pt@#1}{%
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\pgfkeysalso{#3}%
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}{
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\pgfkeysalso{#2}%
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}
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},
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onslide/.code args={<#1>#2}{%
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\only<#1>{\pgfkeysalso{#2}}%
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},
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alt/.code args={<#1>#2#3}{%
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\alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}}%
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},
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stop jumping/.style={
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execute at end picture={%
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\stepcounter{jumping}%
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\immediate\write\pgfutil@auxout{%
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\noexpand\jump@setbb{\the\value{jumping}}{\noexpand\pgfpoint{\the\pgf@picminx}{\the\pgf@picminy}}{\noexpand\pgfpoint{\the\pgf@picmaxx}{\the\pgf@picmaxy}}
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},
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\csname jump@\the\value{jumping}@maxbb\endcsname
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\path (\the\pgf@x,\the\pgf@y);
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\csname jump@\the\value{jumping}@minbb\endcsname
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\path (\the\pgf@x,\the\pgf@y);
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},
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}
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}
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\def\savepointas#1#2{%
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\expandafter\gdef\csname save@pt@#1\endcsname{#2}%
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}
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\def\tmk@labeldef#1,#2\@nil{%
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\def\tmk@label{#1}%
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\def\tmk@def{#2}%
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}
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\tikzdeclarecoordinatesystem{pic}{%
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\pgfutil@in@,{#1}%
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\ifpgfutil@in@%
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\tmk@labeldef#1\@nil
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\else
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\tmk@labeldef#1,\pgfpointorigin\@nil
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\fi
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\@ifundefined{save@pt@\tmk@label}{%
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\tikz@scan@one@point\pgfutil@firstofone\tmk@def
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}{%
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\pgfsys@getposition{\csname save@pt@\tmk@label\endcsname}\save@orig@pic%
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\pgfsys@getposition{\pgfpictureid}\save@this@pic%
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\pgf@process{\pgfpointorigin\save@this@pic}%
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\pgf@xa=\pgf@x
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\pgf@ya=\pgf@y
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\pgf@process{\pgfpointorigin\save@orig@pic}%
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\advance\pgf@x by -\pgf@xa
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\advance\pgf@y by -\pgf@ya
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}%
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}
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\newcommand\tikzmark[2][]{%
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\tikz[remember picture with id=#2] #1;}
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\makeatother
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\resetcounteronoverlays{algocf}
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\newcommand<>{\boxto}[1]{%
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\only#2{\tikz[remember picture with id=#1]
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\draw[line width=1pt,fill=\fillcol,rectangle,rounded corners]
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(pic cs:#1) ++(5.2,-.1) rectangle (-0.4,0)
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;\tikz\node [anchor=base] (#1){};}% <= insertion to store the anchor to be used as based for the annotation
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}
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@ -0,0 +1,84 @@
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\documentclass{article}
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\usepackage[pdftex,active,tightpage]{preview}
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\setlength\PreviewBorder{2mm}
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\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
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\usepackage{braket} % needed for \Set
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\usepackage{algorithm,algpseudocode}
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\begin{document}
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\begin{preview}
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\begin{itemize}
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\item $c:E \rightarrow \mathbb{R}_0^+$: capacity of an edge
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\item $e: V \rightarrow \mathbb{R}_0^+$: excess (too much flow in one node)
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\item $r_f: V \times V \rightarrow \mathbb{R}, \; r_f(u,v) := c(u,v) - f(u,v) $: remaining capacity
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\item $dist: V \rightarrow \mathbb{N}$: the label (imagine this as height)
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\end{itemize}
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\begin{algorithm}[H]
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\begin{algorithmic}
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\Function{PushRelabel}{Network $N(D, s, t, c)$}
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\ForAll{$(v,w) \in (V \times V \setminus E)$} \Comment{If an edge is not in $D=(V,E)$,}
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\State $c(v,w) \gets 0$ \Comment{then its capacity is 0}
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\EndFor
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\\
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\ForAll{$(v,w) \in V \times V$} \Comment{At the beginning, every edge}
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\State $f(v,w) \gets 0$ \Comment{has flow=0}
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\State $r_f(v,w) \gets c(v,w)$ \Comment{flow=max in the residualgraph}
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\EndFor
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\\
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\State $dist(s) \gets |V|$
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\ForAll{$v \in V \setminus \Set{s}$}
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\State $f(s,v) \gets c(s,v)$ \Comment{Push maximum flow out at the beginning}
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\State $r(v,s) \gets c(v,s) - f(v,s)$
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\State $dist(v) \gets 0$
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\State $e(v) \gets c(s,v)$ \Comment{$v$ has to much flow}
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\EndFor
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\\
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\While{$\exists v \in V:$ \Call{isActive}{v}}
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\If{\Call{isPushOk}{v}}
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\State \Call{Push}{v}
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\ElsIf{\Call{isRelabelOk}{v}}
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\State \Call{Relabel}{v}
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\EndIf
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\EndWhile
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\\
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\State \Return $f$ \Comment{Maximaler Fluss}
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\EndFunction
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\\
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\Function{Push}{Graph $D$, Flow $f$, Node $v$, Node $w$}
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\State $\Delta \gets \min\Set{e(v), r_f(v,w)}$
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\State $f(v,w) \gets f(v,w) + \Delta$
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\State $f(w,v) \gets f(w,v) - \Delta$
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\State $r_f(v,w) \gets r_f(v,w) - \Delta$
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\State $r_f(w,v) \gets r_f(w,v) + \Delta$
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\State $e(v) \gets e(v) - \Delta$
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\State $e(w) \gets e(w) + \Delta$
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\EndFunction
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\\
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\Function{Relabel}{Node $v$}
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\If{$\Set{w|r_f(v,w) > 0} == \emptyset$}
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\State $dist(v) \gets \infty$
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\Else
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\State $dist(v) \gets \min\Set{dist(w)+1|w \in V: r_f(v,w) > 0}$
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\EndIf
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\EndFunction
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\\
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\Function{isActive}{Node v}
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\State\Return $(e(v) > 0) \land (dist(v) < \infty)$
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\EndFunction
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\\
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\Function{isRelabelOk}{Node v}
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\State\Return \Call{isActive}{v} $\land (\forall w \in \Set{r_f(v,w) >0}: dist(v) \leq dist(w))$
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\EndFunction
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\\
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\Function{isPushOk}{Node v}
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\State\Return \Call{isActive}{v} $\land (r_f > 0) \land (dist(v) == dist(w)+1)$
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\EndFunction
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\end{algorithmic}
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\caption{Algorithm of Goldberg and Tarjan}
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\label{alg:seq1}
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\end{algorithm}
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\end{preview}
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\end{document}
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35
source-code/Pseudocode/Goldberg-Tarjan-Push-Relabel/Makefile
Normal file
35
source-code/Pseudocode/Goldberg-Tarjan-Push-Relabel/Makefile
Normal file
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SOURCE = Goldberg-Tarjan-Push-Relabel
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DELAY = 80
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DENSITY = 300
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WIDTH = 500
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make:
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pdflatex $(SOURCE).tex -output-format=pdf
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make clean
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clean:
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rm -rf $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
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gif:
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pdfcrop $(SOURCE).pdf
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convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
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make clean
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png:
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make
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make svg
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inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
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transparentGif:
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convert $(SOURCE).pdf -transparent white result.gif
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make clean
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svg:
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make
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#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
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pdf2svg $(SOURCE).pdf $(SOURCE).svg
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# Necessary, as pdf2svg does not always create valid svgs:
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inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg
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rsvg-convert -a -w $(WIDTH) -f svg $(SOURCE).svg -o $(SOURCE)2.svg
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inkscape $(SOURCE)2.svg --export-plain-svg=$(SOURCE).svg
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rm $(SOURCE)2.svg
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