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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).
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