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On Integer Recognition over Some Boolean Quadric Polytope Extension

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Discrete Optimization and Operations Research (DOOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

The problem of integer recognition is to determine whether the maximum of a linear objective function achieved at an integral vertex of a polytope. We consider integer recognition over polytope SATP and its LP relaxation \(SATP_{LP}\). These polytopes are natural extensions of the well-known Boolean quadric polytope BQP and its rooted semimetric relaxation \(BQP_{LP}\).

Integer recognition over \(SATP_{LP}\) is NP-complete, since various special instances of 3-SAT problem like NAE-3SAT and X3SAT are transformed to it. We describe polynomially solvable subproblems of integer recognition over \(SATP_{LP}\) with constrained objective functions. Based on that, we solve some cases of edge constrained bipartite graph coloring.

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Acknowledgments

The research was partially supported by the Russian Foundation for Basic Research, Project 14-01-00333, and the President of Russian Federation Grant MK-5400.2015.1.

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Authors and Affiliations

  1. Department of Discrete Analysis, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia

    Andrei Nikolaev

Authors
  1. Andrei Nikolaev
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Correspondence to Andrei Nikolaev .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

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© 2016 Springer International Publishing Switzerland

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Nikolaev, A. (2016). On Integer Recognition over Some Boolean Quadric Polytope Extension. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_17

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

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