On cut-based inequalities for capacitated network design polyhedra

In this article we study capacitated network design problems. We unify and extend polyhedral results for directed, bidirected and undirected link capacity models. Based on valid inequalities for a network cut we show that regardless of the link capacity model, facets of the polyhedra associated with such a cut translate to facets of the original network design polyhedra if the two subgraphs defined by the network cut are (strongly) connected. Our investigation of the facial structure of the cutset polyhedra allows to complement existing polyhedral results for the three variants by presenting facet-defining flow-cutset inequalities in a unifying way. In addition, we present a new class of facet-defining inequalities, showing as well that flow-cutset inequalities alone do not suffice to give a complete description for single-commodity, singlemodule cutset polyhedra in the bidirected and undirected case – in contrast to a known result for the directed case. The practical importanc...

• Type: Journal
• Year: 2011
• Where: NETWORKS
• Authors: Christian Raack, Arie M. C. A. Koster, Sebastian Orlowski, Roland Wessäly
• Keywords: Computer Networks, Inequalities, Link Capacity Model, Network Design, NETWORKS 2011