The Ford–Fulkerson algorithm (named for L. R. Ford, Jr. and D. R. Fulkerson) computes the maximum flow in a flow network. It was published in 1956. The name "Ford–Fulkerson" is often also used for the Edmonds–Karp algorithm, which is a specialization of Ford–Fulkerson.
The idea behind the algorithm is very simple: As long as there is a path from the source (start node) to the sink (end node), with available capacity on all edges in the path, we s...
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The Ford–Fulkerson algorithm (named for L. R. Ford, Jr. and D. R. Fulkerson) computes the maximum flow in a flow network. It was published in 1956. The name "Ford–Fulkerson" is often also used for the Edmonds–Karp algorithm, which is a specialization of Ford–Fulkerson.
The idea behind the algorithm is very simple: As long as there is a path from the source (start node) to the sink (end node), with available capacity on all edges in the path, we send flow along one of these paths. Then we find another path, and so on. A path with available capacity is called an augmenting path.
Let G(V,E) be a graph, and for each edge from u to v, let c(u,v) be the capacity and f(u,v) = 0 be the flow. We want to find the maximum flow from the source s to the sink t. After every step in the algorithm the following is maintained:
This means that the flow through the network is a legal flow after each round in the algorithm. We define the residual network Gf(V,Ef) to be the network with capacity cf(u,v) =...
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