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Next: Residual Network Up: CSE 2320: Algorithms and Previous: Ford-Fulkerson Method

Residual Capacity

Given flow network G = (V, E) with flow f and two vertices u, v $\in$ V, define the residual capacity cf(u,v) as the additional net flow possible from u to v, not exceeding c(u,v). Thus


\begin{displaymath}c_f(u,v) \;=\; c(u,v) \;-\; f(u,v).\end{displaymath}

Example



\psfig{figure=figures/f19-3.ps}


\begin{displaymath}c_f(s, v_2) \;=\; c(s, v_2) \;-\; f(s, v_2) \;=\; 4 \;-\; 2 \;=\; 2\end{displaymath}


\begin{displaymath}c_f(v_2, t) \;=\; 2 \;-\; 2 \;=\; 0\end{displaymath}


\begin{displaymath}c_f(t, v_2) \;=\; 0 \;-\; (-2) \;=\; 2\end{displaymath}



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