Polyhedral results for two-connected networks with bounded rings

We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a ‘ring’) does not exceed a given length K. We present here a new formulation of the problem and derive facet results for different classes of valid inequalities. We study the separation problems associated to these inequalities and their integration in a Branch-and-Cut algorithm, and provide extensive computational results.