Mathematical
Programming
 		Ford-Fulkerson's Algorithm

Simplex

Twophase

Dijkstra

Prim

Kruskal

Ford-Fulkerson

Ford-Fulkerson
Java applet demos:
FAQ
Japanese/English

Maximum Flow Problem

Given a connected graph G=(V,E), a capacity c:E->R+, and two nodes s and t, find a maximum s-t flow.

Minimum Cut Problem

Given a connected graph G=(V,E), a capacity c:E->R+, and two nodes s and t, find a minimum s-t cut.

Ford-Fulkerson Labeling Algorithm

  1. (Initialization) Let x be an initial feasible flow (e.g. x(e) = 0 for all e in E).
  2. (Flow augmentation) If there are no augmenting path from s to t on the residual network, then stop. The present x is a max flow. If there is a flow augmenting path p, replace the flow x as
    • x(e)=x(e)+delta if e is a forward arc on p.
    • x(e)=x(e)-delta if e is a backward arc on p.
    where delta is a minimum value of residual capacity on p. Repeat this step.

Java Source files:

Java Applet Demos

Here is a JAVA applet illustrating the Ford-Fulkerson Labeling Algorithm, which yields a max-flow and a min-cut.

See Also

Kenji Ikeda's
Home Page		 Last Modified: Wednesday, 07-Jun-2000 16:24:59 JST