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Multicommodity Flows in Even, Planar Networks

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Abstract.

We consider the problem of finding an integral multicommodity flow in a planar, undirected graph where all sources and all targets are on the boundary of the infinite face. Moreover, all capacities and all demands satisfy the so-called evenness condition. The best algorithm known so far requires \({\cal O}(kn+n^2)\) time, where n denotes the number of vertices and k the number of source—target pairs. In this paper we introduce an algorithm that is based on a completely new approach and is asymptotically optimal, that is, requires only \({\cal O}(kn)\) time in the worst case.

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Received April 20, 1994; revised June 21, 1995.

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Weihe, K. Multicommodity Flows in Even, Planar Networks . Algorithmica 18, 363 (1997). https://doi.org/10.1007/PL00009161

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  • DOI: https://doi.org/10.1007/PL00009161

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