A Branch and Cut solver for the maximum stable set problem

Authors:
Steffen Rebennack;Marcus Oswald;Dirk Oliver Theis;Hanna Seitz;Gerhard Reinelt;Panos M. Pardalos
Affiliations:
Department of Industrial & Systems Engineering, University of Florida, Gainesville, USA;Discrete Optimization Research Group, Ruprecht-Karls Universität Heidelberg, Heidelberg, Germany;Fakultät für Mathematik (IMO), OvG-Universität Magdeburg, Magdeburg, Germany;Discrete Optimization Research Group, Ruprecht-Karls Universität Heidelberg, Heidelberg, Germany;Discrete Optimization Research Group, Ruprecht-Karls Universität Heidelberg, Heidelberg, Germany;Department of Industrial & Systems Engineering, University of Florida, Gainesville, USA
Venue:
Journal of Combinatorial Optimization
Year:
2011

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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.