Journal of Combinatorial Optimization

, Volume 21, Issue 4, pp 434–457

A Branch and Cut solver for the maximum stable set problem

  • Steffen Rebennack
  • Marcus Oswald
  • Dirk Oliver Theis
  • Hanna Seitz
  • Gerhard Reinelt
  • Panos M. Pardalos
Article

DOI: 10.1007/s10878-009-9264-3

Cite this article as:
Rebennack, S., Oswald, M., Theis, D.O. et al. J Comb Optim (2011) 21: 434. doi:10.1007/s10878-009-9264-3

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.

Keywords

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

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Steffen Rebennack
    • 1
  • Marcus Oswald
    • 2
  • Dirk Oliver Theis
    • 3
  • Hanna Seitz
    • 2
  • Gerhard Reinelt
    • 2
  • Panos M. Pardalos
    • 1
  1. 1.Department of Industrial & Systems EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Discrete Optimization Research GroupRuprecht-Karls Universität HeidelbergHeidelbergGermany
  3. 3.Fakultät für Mathematik (IMO)OvG-Universität MagdeburgMagdeburgGermany