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Flowgorithm is a graphical authoring tool which allows users to write and execute programs using flowcharts.The approach is designed to emphasize the algorithm rather than the syntax of a specific programming language. [1]
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.
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, Dinitz kept working on flow algorithms. He wrote a Moscow State University Ph.D. thesis on commodity flow problems, which he submitted in 1972. [ 16 ] [ 17 ] He developed the idea of capacity scaling independently of Edmonds and Karp , who had just introduced it in the West, and he used it to invent one of the first polynomial-time ...
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 ...
The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network.A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated.