Using Symmetry to Optimize Over the Sherali-Adams Relaxation

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


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.


Extended Formulation Valid Inequality Linear Program Relaxation Quadratic Assignment Problem Linear Program Formulation 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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