The multi-terminal vertex separator problem: Extended formulations and Branch-and-Cut-and-Price

Abstract

In this paper we discuss a variant of the well-known k-separator problem. Given a simple graph G = (V ∪ T, E) with V ∪ T the set of vertices, where T is a set of distinguished vertices called terminals, and E a set of edges, the multi-terminal vertex separator problem consists in partitioning V ∪T into k+1 subsets {S, V 1 , …, V k } such that the size of S is minimum, each subset V i contains exactly one terminal and no vertex in V i is adjacent to a vertex in V j . Three extended formulations are proposed for the problem. We develop Branch-and-Price algorithms for the two first formulations and a Branch-and-Cut-and-Price algorithm for the third one. Some experimental results are also discussed.