The maximum flow problem is log space complete for P

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The maximum flow problem

In this network we have two special vertices: a source vertex s and a sink vertex t. Our goal is to send the maximum amount of flow from s to t; flow can only travel along arcs in the right direction, and is constrained by the arc capacities. This “flow” could be many things: imagine sending water along pipes, with the capacity representing the size of the pipe; or traffic, with the capacity be...

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We prove that the maximum edge biclique problem in bipartite graphs is NP-complete. A biclique in a bipartite graph is a vertex induced subgraph which is complete. The problem of finding a biclique with a maximum number of vertices is known to be solvable in polynomial time but the complexity of finding a biclique with a maximum number of edges was still undecided.

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Recently, Goldberg proposed a new approach lo the maximum netv.ork flow problem. The approach yields a ver>' simple algorithm nmning in 0{n^) time on n-vertex networks. Incorporation of the dynamic tree data structure of Sleator and Tarjan yields a more complicated algorithm with a running time of 0{rvn log {n^ Im)) on m-arc networks. Ahuja and Orlin developed a variant of Goldberg's algorithm ...

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In several applications of network flows, additional constraints have to be considered. In this paper, we study flows, where the flow particles have an orientation. For example, cargo containers with doors only on one side and train coaches with 1st and 2nd class compartments have such an orientation. If the end position has a mandatory orientation, not every path from source to sink is feasibl...

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ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 1982

ISSN: 0304-3975

DOI: 10.1016/0304-3975(82)90092-5