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Using Symmetry to Optimize Over the Sherali-Adams Relaxation

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Combinatorial Optimization (ISCO 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7422))

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Abstract

In this paper we examine the impact of using the Sherali-Adams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations generated by Sherali-Adams can be very large, containing \(O(\binom{n}{d})\) many variables for the level-d closure. When large amounts of symmetry are present in the problem instance however, the symmetry can be used to generate a much smaller linear program that has an identical objective value. We demonstrate this by computing the bound associated with the level 1, 2, and 3 relaxations of several highly symmetric binary integer programming problems. We also present a class of constraints, called counting constraints, that further improves the bound, and in some cases provides a tight formulation.

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Author information

Authors and Affiliations

  1. University of Tennessee, Knoxville, TN, 37996, USA

    James Ostrowski

Authors
  1. James Ostrowski
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Editor information

Editors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    A. Ridha Mahjoub  & Vangelis Th. Paschos  & 

  2. Department of Informatics, Athens University of Economics and Business, 76 Patission str., 10434, Athens, Greece

    Vangelis Markakis  & Ioannis Milis  & 

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Ostrowski, J. (2012). Using Symmetry to Optimize Over the Sherali-Adams Relaxation. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-32147-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32146-7

  • Online ISBN: 978-3-642-32147-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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