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Mincut ideals of two-terminal networks

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

This paper introduces mincut ideals of two-terminal networks, which arise in the algebraic analysis of system reliability. We give the definitions and study their algebraic and combinatorial properties in some particular cases. It turns out that some features of the mincut ideals arising from networks such as the Cohen-Macaulay property and the computation of Betti numbers, which are important in tight reliability bounds, have a compact expression for series-parallel networks. This relies on a natural mapping of the structure of such networks into the union and intersection structure of the corresponding ideal.

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Authors and Affiliations

  1. Universidad de La Rioja, La Rioja, Spain

    Eduardo Sáenz-de-Cabezón

  2. London School of Economics, London, UK

    Henry P. Wynn

Authors
  1. Eduardo Sáenz-de-Cabezón
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  2. Henry P. Wynn
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Correspondence to Eduardo Sáenz-de-Cabezón.

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Sáenz-de-Cabezón, E., Wynn, H.P. Mincut ideals of two-terminal networks. AAECC 21, 443–457 (2010). https://doi.org/10.1007/s00200-010-0132-2

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  • DOI: https://doi.org/10.1007/s00200-010-0132-2

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