Search results
Results From The WOW.Com Content Network
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 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 ...
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 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
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.
In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961, [1] and published in 1965. [2] Given a general graph G = (V, E), the algorithm finds a matching M such that each vertex in V is incident with at most one edge in M and | M | is maximized. The ...
The algorithm was discovered by John Hopcroft and Richard Karp and independently by Alexander Karzanov . [3] As in previous methods for matching such as the Hungarian algorithm and the work of Edmonds (1965), the Hopcroft–Karp algorithm repeatedly increases the size of a partial matching by finding augmenting paths. These paths are sequences ...