The Ford–Fulkerson algorithm is a method used to compute the maximum flow in a flow network. Developed by L.R. Ford, Jr. and D.R. Fulkerson in the 1950s, this algorithm is based on the concept of augmenting paths and works by iteratively increasing the flow in the network until no more augmenting paths can be found.
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The Ford-Fulkerson algorithm repeatedly augments a feasible flow along an augmenting path. When no such path remains, the source-reachable vertices in the residual network define a cut of capacity equal to the flow value, proving optimality by the max-flow min-cut theorem.