Two-connected networks with rings of bounded cardinality

We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli. In this paper, we compute a lower bound on the … Read more

Mesh Topology Design in Overlay Virtual Private Networks

We study the mesh topology design problem in overlay virtual private networks. Given a set of customer nodes and associated traffic matrix, tunnels that are connecting node pairs through a public service provider network subject to degree constraints are determined so as to minimize total multihopped traffic. Valid inequalities strengthening the LP relaxation and a … Read more

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 … Read more

Branch-and-cut for the k-way equipartition problem

We investigate the polyhedral structure of a formulation of the k-way equipartition problem and a branch-and-cut algorithm for the problem. The k-way equipartition problem requires dividing the vertices of a weighted graph into k equally sized sets, so as to minimize the total weight of edges that have both endpoints in the same set. Applications … Read more