A class of web-based facets for the generalized vertex packing problem

Authors:
Hanif D. Sherali;J. Cole Smith
Affiliations:
Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA;Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

The generalized vertex packing problem seeks to identify a largest subset of nodes from an undirected graph, such that the subgraph induced by this subset of nodes contains no more than some threshold number of edges. This paper derives a class of valid inequalities based on certain special subgraphs called webs, which are general structures that subsume cliques, matchings, odd holes, and odd anti-holes. We also provide a set of conditions for this class of valid inequalities to be facet-inducing for the web subgraph polytope. Finally, we prescribe a web subgraph identification procedure, and test the computational benefits obtained by solving generalized vertex packing instances with formulations augmented by these web-based valid inequalities.