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In computer science, the Edmonds–Karp algorithm is an implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network in (| | | |) time. The algorithm was first published by Yefim Dinitz in 1970, [ 1 ] [ 2 ] and independently published by Jack Edmonds and Richard Karp in 1972. [ 3 ]
The Edmonds–Karp algorithm, a faster strongly polynomial algorithm for maximum flow; The Ford–Fulkerson algorithm, a greedy algorithm for maximum flow that is not in general strongly polynomial; The network simplex algorithm, a method based on linear programming but specialized for network flow [1]: 402–460
Over the years, various improved solutions to the maximum flow problem were discovered, notably the shortest augmenting path algorithm of Edmonds and Karp and independently Dinitz; the blocking flow algorithm of Dinitz; the push-relabel algorithm of Goldberg and Tarjan; and the binary blocking flow algorithm of Goldberg and Rao.
Dinitz's algorithm and the Edmonds–Karp algorithm (published in 1972) both independently showed that in the Ford–Fulkerson algorithm, if each augmenting path is the shortest one, then the length of the augmenting paths is non-decreasing and the algorithm always terminates.
The complete Karmarkar–Karp algorithm (CKK) finds an optimal solution by constructing a tree of degree !. In the case k =2, each level corresponds to a pair of numbers, and the two branches correspond to taking their difference (i.e. putting them in different sets), or taking their sum (i.e. putting them in the same set).
The first three stages of Johnson's algorithm are depicted in the illustration below. The graph on the left of the illustration has two negative edges, but no negative cycles. The center graph shows the new vertex q, a shortest path tree as computed by the Bellman–Ford algorithm with q as starting vertex, and the values h(v) computed at each other node as the length of the shortest path from ...
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Edmonds's algorithm ( edmonds-alg ) – An implementation of Edmonds's algorithm written in C++ and licensed under the MIT License. This source is using Tarjan's implementation for the dense graph. NetworkX, a python library distributed under BSD, has an implementation of Edmonds' Algorithm.