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Combinatorial properties of noninteger vertices of a polytope in a three-index axial assignment problem

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Abstract

It is proved that, for any r ∈ { 2n, 2n + 1,…, 3n−2} and only for such r, the polytope of a three-index axial assignment problem of order n, n ≥ 2, contains completely r-noninteger vertices (r-CNVs), i.e., vertices such that all their positive components are fractional and their number equals r. For each r ∈ {2n, 2n + 1,…, 3n −2}, all the types of r-CNVs are characterized and the combinatorial properties of completely r-noninteger vertices of the polytope are studied.

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  1. Belarus State University, Minsk, Byelorussia

    V. M. Kravtsov

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  1. V. M. Kravtsov
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 33–44, January–February 2007.

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Kravtsov, V.M. Combinatorial properties of noninteger vertices of a polytope in a three-index axial assignment problem. Cybern Syst Anal 43, 25–33 (2007). https://doi.org/10.1007/s10559-007-0023-0

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  • DOI: https://doi.org/10.1007/s10559-007-0023-0

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