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A Branch and Cut solver for the maximum stable set problem

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Abstract

This paper deals with the cutting-plane approach to the maximum stable set problem. We provide theoretical results regarding the facet-defining property of inequalities obtained by a known project-and-lift-style separation method called edge-projection, and its variants. An implementation of a Branch and Cut algorithm is described, which uses edge-projection and two other separation tools which have been discussed for other problems: local cuts (pioneered by Applegate, Bixby, Chvátal and Cook) and mod-k cuts. We compare the performance of this approach to another one by Rossi and Smiriglio (Oper. Res. Lett. 28:63–74, 2001) and discuss the value of the tools we have tested.

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Authors and Affiliations

  1. Department of Industrial & Systems Engineering, University of Florida, Gainesville, FL, USA

    Steffen Rebennack & Panos M. Pardalos

  2. Discrete Optimization Research Group, Ruprecht-Karls Universität Heidelberg, Heidelberg, Germany

    Marcus Oswald, Hanna Seitz & Gerhard Reinelt

  3. Fakultät für Mathematik (IMO), OvG-Universität Magdeburg, Magdeburg, Germany

    Dirk Oliver Theis

Authors
  1. Steffen Rebennack
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  2. Marcus Oswald
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  3. Dirk Oliver Theis
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  4. Hanna Seitz
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  5. Gerhard Reinelt
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  6. Panos M. Pardalos
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Corresponding author

Correspondence to Steffen Rebennack.

Additional information

Panos M. Pardalos is partially supported by Airfoce and DTRA grants.

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Rebennack, S., Oswald, M., Theis, D.O. et al. A Branch and Cut solver for the maximum stable set problem. J Comb Optim 21, 434–457 (2011). https://doi.org/10.1007/s10878-009-9264-3

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  • DOI: https://doi.org/10.1007/s10878-009-9264-3

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