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The maximum flow problem in a network with special conditions of flow distribution

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Abstract

We consider the problem of finding a maximum flow in networks with strictly and nonstrictly determined flow distribution. We show that, for each condition of flow distribution, a solution to the problem under consideration exists and is unique. Some algorithms for finding a maximum flow are developed for each condition of flow distribution. We find bounds for the maximum flow value in networks with strict flow distribution.

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Authors and Affiliations

  1. Southern Federal University, ul. Milchakova 8a, Rostov-on-Don, 344090, Russia

    V. A. Skorokhodov & A. S. Chebotareva

Authors
  1. V. A. Skorokhodov
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  2. A. S. Chebotareva
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Correspondence to V. A. Skorokhodov.

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Original Russian Text © V.A. Skorokhodov, A.S. Chebotareva, 2015, published in Diskretnyi Analiz i Issledovanie Operatsii, 2015, Vol. 22, No. 3, pp. 55–73.

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Skorokhodov, V.A., Chebotareva, A.S. The maximum flow problem in a network with special conditions of flow distribution. J. Appl. Ind. Math. 9, 435–446 (2015). https://doi.org/10.1134/S199047891503014X

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  • DOI: https://doi.org/10.1134/S199047891503014X

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