A Branch and Cut solver for the maximum stable set problem

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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Correspondence to Steffen Rebennack.

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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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Keywords

  • Maximum stable set problem
  • Cutting-plane algorithm
  • Branch and Cut
  • Separation algorithm
  • Edge-projection