Approche polyedrale pour le probleme du separateur (VSP)

The vertex separator problem (VSP) in an undirected connected graph G = (V,E) asks for a partition of V into nonempty subsets A, B, C such that |C| is minimized subject to there is no edge between A and B, and max{|A|, |B|} ≤ β(n) with β(n) integer such as 1 ≤ β(n) ≤ n. We investigate the (VSP) in a polyhedral way, starting from the formulation given by E. Balas and C. De Souza [1]. We introduce new efficient valid inequalities. Our algorithm is based on some of the inequalities discussed here. The power of these inequalities is illustrated by the computational tests, efficiently improving the Balas and De Souza’s results [2].