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Using Symmetry to Optimize Over the Sherali-Adams Relaxation

  • James Ostrowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)

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.

Keywords

Extended Formulation Valid Inequality Linear Program Relaxation Quadratic Assignment Problem Linear Program Formulation 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • James Ostrowski
    • 1
  1. 1.University of TennesseeKnoxvilleUSA

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