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Theoretical improvements in algorithmic efficiency for network flow problems (1972)

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by Jack Edmonds , Richard M. Karp
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Citations:559 - 0 self
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BibTeX

@MISC{Edmonds72theoreticalimprovements,
    author = {Jack Edmonds and Richard M. Karp},
    title = {Theoretical improvements in algorithmic efficiency for network flow problems},
    year = {1972}
}

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Abstract

This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem. Upper bounds on ... the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps required by earlier algorithms. First, the paper states the maximum flow problem, gives the Ford-Fulkerson labeling method for its solution, and points out that an improper choice of flow augmenting paths can lead to severe computational difficulties. Then rules of choice that avoid these difficulties are given. We show that, if each flow augmentation is made along an augmenting path having a minimum number of arcs, then a maximum flow in an n-node network will be obtained after no more than ~(n a- n) augmentations; and then we show that if each flow change is chosen to produce a maximum increase in the flow value then, provided the capacities are integral, a maximum flow will be determined within at most 1 + logM/(M--1) if(t, S) augmentations, wheref*(t, s) is the value of the maximum flow and M is the maximum number of arcs across a cut. Next a new algorithm is given for the minimum-cost flow problem, in which all shortest-path computations are performed on networks with all weights nonnegative. In particular, this

Keyphrases

theoretical improvement    network flow problem    maximum flow    algorithmic efficiency    maximum flow problem    new algorithm    general minimum-cost flow problem    n-node network    ford-fulkerson labeling method    shortest-path computation    minimum number    upper bound    flow augmentation    severe computational difficulty    maximum number    improper choice    hitchcock transportation problem    minimum-cost flow problem    flow change    maximum increase    flow value   

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