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The width and integer optimization on simplices with bounded minors of the constraint matrices

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Abstract

In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some quasi-polynomial-time and polynomial-time algorithms to solve the integer linear optimization problem defined on simplices minus all their integer vertices assuming that some minors of the constraint matrices of the simplices are bounded.

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Acknowledgments

This research is partially supported by Russian Foundation for Basic Research, Grants No 16-31-00109-mol-a and No 15-01-06249-A, by RF President Grant MK-4819.2016.1, by LATNA laboratory, National Research University Higher School of Economics. The first author would like to thank Prof. P.M. Pardalos and his academic supervisor Prof. D.S. Malyshev.

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Authors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, 23 Gagarina Avenue, Nizhny Novgorod, 603950, Russian Federation

    D. V. Gribanov & A. Y. Chirkov

  2. National Research University Higher School of Economics, 136 Rodionova, Nizhny Novgorod, 603093, Russian Federation

    D. V. Gribanov

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  1. D. V. Gribanov
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  2. A. Y. Chirkov
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Correspondence to D. V. Gribanov.

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Gribanov, D.V., Chirkov, A.Y. The width and integer optimization on simplices with bounded minors of the constraint matrices. Optim Lett 10, 1179–1189 (2016). https://doi.org/10.1007/s11590-016-1048-y

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  • DOI: https://doi.org/10.1007/s11590-016-1048-y

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