The Multi-Terminal Vertex Separator Problem: Branch-And-Cut-And-Price

We are given a graph G = (V boolean OR T, E), with V boolean OR T the set of vertices where T is a set of terminals and E the set of edges. The multi-terminal vertex separator problem consists in finding a subset of vertices S subset of V of minimum size intersecting all paths between every pair of terminals. In this paper we present three extended linear integer programming formulations for the multi-terminal vertex separator problem and we develop Branch-and-Price and Branch-and-Cut-and-Price algorithms. For each formulation we present the pricing problem, the branching scheme and the computation of the dual bound used during the column generation phase. Computational results are reported comparing the performance of the formulations on a set of instances. (C) 2020 Published by Elsevier B.V.