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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]
This means all v ∈ V \ {s, t} have no excess flow, and with no excess the preflow f obeys the flow conservation constraint and can be considered a normal flow. This flow is the maximum flow according to the max-flow min-cut theorem since there is no augmenting path from s to t. [8] Therefore, the algorithm will return the maximum flow upon ...
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.
Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim Dinitz. [1]
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 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 push–relabel maximum flow algorithm, one of the ...
Some of them are generalizations of maximum flow algorithms, others use entirely different approaches. Well-known fundamental algorithms (they have many variations): Cycle canceling: a general primal method. [2] Cut canceling: a general dual method. [3] [4] Minimum mean cycle canceling: a simple strongly polynomial algorithm. [5]
Flow networks. Dinic's algorithm: is a strongly polynomial algorithm for computing the maximum flow in a flow network. Edmonds–Karp algorithm: implementation of Ford–Fulkerson; Ford–Fulkerson algorithm: computes the maximum flow in a graph; Karger's algorithm: a Monte Carlo method to compute the minimum cut of a connected graph