The Ford–Fulkerson algorithm Michael Tehranchi

This slideshow illustrates the Ford–Fulkerson algorithm for find-ing a maximal flow through a network.

(0) Assign an initial feasible flow (xij)i,j∈N with value v..

(1) Find an augmenting path 1 = i1, i2, . . . , ir−1, ir = n from node1 to node n.

If no augmenting path exists, then STOP. The flow (xij)i,j∈N isoptimal and there exists a cut with capacity v.

(2) If an augmenting path exists, then increase the flow alongthe path by the amount

δ = mink=1,...,r−1

max{cikik+1− xikik+1

, xik+1ik}

by setting

x′ij =

xij + δ if i, j are consecutive nodes of pathxij − δ if j, i are consecutive nodes of path

xij otherwise

Then (x′ij)i,j∈N is a feasible flow with value v′ = v + δ.

(3) Go to step (1).