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International Conference on Discrete Optimization and Operations Research

DOOR 2016: Discrete Optimization and Operations Research pp 206–219Cite as

On Integer Recognition over Some Boolean Quadric Polytope Extension

Part of the Lecture Notes in Computer Science book series (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.

Keywords

  • Truth Assignment
  • Objective Vector
  • Extension Complexity
  • Linear Objective Function
  • Integral Vertex

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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

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  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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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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