diff --git a/source-code/Pseudocode/Goldberg-Tarjan-Push-Relabel/Goldberg-Tarjan-Push-Relabel.tex b/source-code/Pseudocode/Goldberg-Tarjan-Push-Relabel/Goldberg-Tarjan-Push-Relabel.tex index 271dbb6..7c7aedb 100644 --- a/source-code/Pseudocode/Goldberg-Tarjan-Push-Relabel/Goldberg-Tarjan-Push-Relabel.tex +++ b/source-code/Pseudocode/Goldberg-Tarjan-Push-Relabel/Goldberg-Tarjan-Push-Relabel.tex @@ -33,21 +33,22 @@ \State $f(s,v) \gets c(s,v)$ \Comment{Push maximum flow out at the beginning} \State $r(v,s) \gets c(v,s) - f(v,s)$ \State $dist(v) \gets 0$ - \State $e(v) \gets c(s,v)$ \Comment{$v$ has to much flow} + \State $e(v) \gets c(s,v)$ \Comment{$v$ has too much flow} \EndFor \\ - \While{$\exists v \in V:$ \Call{isActive}{v}} - \If{\Call{isPushOk}{v}} - \State \Call{Push}{v} - \ElsIf{\Call{isRelabelOk}{v}} - \State \Call{Relabel}{v} + \While{$\exists v \in V:$ \Call{isActive}{$v$}} + \If{\Call{isPushOk}{$v$}} + \State \Call{Push}{$v$} + \EndIf + \If{\Call{isRelabelOk}{$v$}} + \State \Call{Relabel}{$v$} \EndIf \EndWhile \\ \State \Return $f$ \Comment{Maximaler Fluss} \EndFunction \\ - \Function{Push}{Graph $D$, Flow $f$, Node $v$, Node $w$} + \Function{Push}{Node $v$, Node $w$} \State $\Delta \gets \min\Set{e(v), r_f(v,w)}$ \State $f(v,w) \gets f(v,w) + \Delta$ \State $f(w,v) \gets f(w,v) - \Delta$ @@ -65,16 +66,16 @@ \EndIf \EndFunction \\ - \Function{isActive}{Node v} + \Function{isActive}{Node $v$} \State\Return $(e(v) > 0) \land (dist(v) < \infty)$ \EndFunction \\ - \Function{isRelabelOk}{Node v} - \State\Return \Call{isActive}{v} $\land (\forall w \in \Set{r_f(v,w) >0}: dist(v) \leq dist(w))$ + \Function{isRelabelOk}{Node $v$} + \State\Return \Call{isActive}{$v$} $\displaystyle \bigwedge_{w \in \Set{w \in V | r_f(v,w) >0}}(dist(v) \leq dist(w))$ \EndFunction \\ - \Function{isPushOk}{Node v} - \State\Return \Call{isActive}{v} $\land (r_f > 0) \land (dist(v) == dist(w)+1)$ + \Function{isPushOk}{Node $v$} + \State\Return \Call{isActive}{$v$} $\land (e(v) > 0) \land (dist(v) == dist(w)+1)$ \EndFunction \end{algorithmic} \caption{Algorithm of Goldberg and Tarjan}