An Integer Polytope Related to the Design of Survivable Communication Networks
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The problem of designing communication networks that can survive the loss of any single link is studied. Such problems can be formulated as minimum cost 2-edge connected subgraph problems in a complete graph. The linear programming cutting plane approach has been used effectively for related problems in [Schwerpunktprogramm der Deutschen Forschungsgemeinschaft, Anwendungsbezogene Optimierung and Steuerung, Report No. 188, 1989], where problem-specific cutting planes that define facets of the underlying integer polyhedra are used. This paper introduces a new class of valid inequalities for the polytope associated with the minimum cost 2-edge connected subgraph problem, and necessary and sufficient conditions for these inequalities to be facet-inducing for this polytope are given.