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The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network.It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified [1] or it is specified in several implementations with different running times. [2]
The maximum flow problem was first formulated in 1954 by T. E. Harris and F. S. Ross as a simplified model of Soviet railway traffic flow. [1] [2] [3]In 1955, Lester R. Ford, Jr. and Delbert R. Fulkerson created the first known algorithm, the Ford–Fulkerson algorithm.
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]
More specifically, capacity function c f of each arc (u, v) in the residual network represents the amount of flow which can be transferred from u to v given the current state of the flow within the network. This concept is used in Ford–Fulkerson algorithm which computes the maximum flow in a flow network.
Also, the flow was obtained by Ford-Fulkerson algorithm, so it is the max-flow of the network as well. Also, since any flow in the network is always less than or equal to capacity of every cut possible in a network, the above described cut is also the min-cut which obtains the max-flow.
Lester Randolph Ford Jr. (September 23, 1927 – February 26, 2017) was an American mathematician specializing in network flow problems. He was the son of mathematician Lester R. Ford Sr. [ 1 ] Ford's paper with D. R. Fulkerson on the maximum flow problem and the Ford–Fulkerson algorithm for solving it, published as a technical report in 1954 ...
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 out-of-kilter algorithm for minimum-cost flow [1]: 326–331
The simplest way to compute a maximum cardinality matching is to follow the Ford–Fulkerson algorithm. This algorithm solves the more general problem of computing the maximum flow. A bipartite graph (X + Y, E) can be converted to a flow network as follows. Add a source vertex s; add an edge from s to each vertex in X.