next up previous
Next: Augmenting Paths Up: CSE 2320: Algorithms and Previous: Residual Capacity

Residual Network

Given flow network G = (V, E) and flow f, the residual network of G induced by f is \(G_f \;=\; (V, E_f)\) where

\begin{displaymath}E_f \;=\; \{(u,v) \;\in\; V x V \;\mid\; c_f(u,v) \;>\; 0\}\end{displaymath}

(u,v) $\in E_f$ is a residual edge; i.e., any edge that can admit more flow.



\psfig{figure=figures/f19-4.ps}

If there is a path from s to t in the residual network, then it is an augmenting path and indicates where flow can increase.



Copyright © 1998 The University of Texas at Arlington