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Next: Corollary 27.4 Up: CSE 2320: Algorithms and Previous: Residual Network

Augmenting Paths

Given flow network G and flow f, an augmenting path p is a simple path from s to t in the residual network Gf.

The minimum net flow along path p in Gf indicates the amount flow can increase along this path in G.

Thus, define the residual capacity of path p as

\begin{displaymath}c_f(p) \;=\; min\{c_f(u,v) \;\mid\; (u,v) \;{\rm is} \;{\rm on} \;p\}\end{displaymath}

Define flow fp in Gf as

\begin{displaymath}f_p(u,v) \;=\; \left\{ \begin{array}{cl} c_f(p) & {\rm if} \;...
...,u) \;{\rm on} \;p \\
0 & {\rm otherwise} \end{array} \right.\end{displaymath}

\begin{displaymath}\mid f_p \mid \;=\; c_f(p) \;>\; 0\end{displaymath}

Define flow sum f1 + f2 as \((f_1 + f_2)(u,v) \;=\;
f_1(u,v) \;+\; f_2(u,v)\).

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