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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] Dinitz's algorithm includes ...
Complexity Description Linear programming: Constraints given by the definition of a legal flow. See the linear program here. Ford–Fulkerson algorithm: 1955 As long as there is an open path through the residual graph, send the minimum of the residual capacities on that path. Edmonds–Karp algorithm: 1970
The name "Ford–Fulkerson" is often also used for the Edmonds–Karp algorithm, which is a fully defined implementation of the Ford–Fulkerson method. The idea behind the algorithm is as follows: 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 ...
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
Time complexity (with n nodes and m arcs) Dinic's algorithm: 1970: O(mn 2) Edmonds–Karp algorithm: 1972: O ... In a source localization problem, an algorithm tries ...
The push–relabel algorithm is considered one of the most efficient maximum flow algorithms. The generic algorithm has a strongly polynomial O(V 2 E) time complexity, which is asymptotically more efficient than the O(VE 2) Edmonds–Karp algorithm. [2] Specific variants of the algorithms achieve even lower time complexities.
However, this analysis does not depend on finding a path that has the exact maximum of capacity; any path whose capacity is within a constant factor of the maximum suffices. Combining this approximation idea with the shortest path augmentation method of the Edmonds–Karp algorithm leads to a maximum flow algorithm with running time O(mn log U ...
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.