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An application of the Lovász–Schrijver M(K, K) operator to the stable set problem

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Abstract

Although the lift-and-project operators of Lovász and Schrijver have been the subject of intense study, their M(K, K) operator has received little attention. We consider an application of this operator to the stable set problem. We begin with an initial linear programming (LP) relaxation consisting of clique and non-negativity inequalities, and then apply the operator to obtain a stronger extended LP relaxation. We discuss theoretical properties of the resulting relaxation, describe the issues that must be overcome to obtain an effective practical implementation, and give extensive computational results. Remarkably, the upper bounds obtained are sometimes stronger than those obtained with semidefinite programming techniques.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università Di L’Aquila, Via Vetoio, 67010, Coppito, AQ, Italy

    Monia Giandomenico, Fabrizio Rossi & Stefano Smriglio

  2. Department of Management Science, Lancaster University Management School, Lancaster, LA1 4YX, UK

    Adam N. Letchford

Authors
  1. Monia Giandomenico
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  2. Adam N. Letchford
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  3. Fabrizio Rossi
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  4. Stefano Smriglio
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Correspondence to Adam N. Letchford.

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Giandomenico, M., Letchford, A.N., Rossi, F. et al. An application of the Lovász–Schrijver M(K, K) operator to the stable set problem. Math. Program. 120, 381–401 (2009). https://doi.org/10.1007/s10107-008-0219-8

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  • DOI: https://doi.org/10.1007/s10107-008-0219-8

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