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A note on polylinking flow networks

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Abstract

This is a supplementary note on M. X. Goemans, S. Iwata, and R. Zenklusen’s paper that proposes a flow model based on polylinking systems. Their flow model is a series (or tandem) connection of polylinking systems. We can consider an apparently more general model of a polylinking flow network which consists of an ordinary arc-capacitated network endowed with polylinking systems on the vertex set, one for each vertex of the network. This is a natural, apparent generalization of polymatroidal flow model of E. L. Lawler and C. U. Martel and of generalized-polymatroidal flow model of R. Hassin. We give a max-flow min-cut formula for the polylinking network flow problem and discuss some acyclic flow property of polylinking flows.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Satoru Fujishige

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  1. Satoru Fujishige
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Correspondence to Satoru Fujishige.

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Research partly supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports and Technology of Japan.

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Fujishige, S. A note on polylinking flow networks. Math. Program. 137, 601–607 (2013). https://doi.org/10.1007/s10107-011-0502-y

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  • DOI: https://doi.org/10.1007/s10107-011-0502-y

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