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k-Sum decomposition of strongly unimodular matrices

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Abstract

Networks are frequently studied algebraically through matrices. In this work, we show that networks may be studied in a more abstract level using results from the theory of matroids by establishing connections to networks by decomposition results of matroids. First, we present the implications of the decomposition of regular matroids to networks and related classes of matrices, and secondly we show that strongly unimodular matrices are closed under k-sums for \(k=1,2\) implying a decomposition into highly connected network-representing blocks, which are also shown to have a special structure.

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Acknowledgments

Work of the second author was conducted at National Research University Higher School of Economics and supported by RSF Grant 14-41-00039.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece

    K. Papalamprou & L. Pitsoulis

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  1. K. Papalamprou
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  2. L. Pitsoulis
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Correspondence to L. Pitsoulis.

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Papalamprou, K., Pitsoulis, L. k-Sum decomposition of strongly unimodular matrices. Optim Lett 11, 407–418 (2017). https://doi.org/10.1007/s11590-015-0975-3

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  • DOI: https://doi.org/10.1007/s11590-015-0975-3

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