The vertex k-cut problem

Denis Cornaz (1) , Fabio Furini (1) , Mathieu Lacroix (2) , Enrico Malaguti (3) , A. Ridha Mahjoub (1) , Sébastien Martin (4)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 LIPN - Laboratoire d'Informatique de Paris-Nord
3 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
4 LCOMS - Laboratoire de Conception, Optimisation et Modélisation des Systèmes

Given an undirected graph G=(V, E), a vertex k-cut of G is a vertex subset of the removing of which disconnects the graph in at least components. Given a graph and an integer k≥2, the vertex k-cut problem consists in finding a vertex k-cut of of G minimum cardinality. We first prove that the problem is NP-hard for any fixed k≥3. We then present a compact formulation, and an extended formulation from which we derive a column generation and a branching scheme. Extensive computational results prove the effectiveness of the proposed methods.

Mots clés: Vertex cut; Mixed-integer programming models; Branch and Price; Exact algorithms

Domaines: Informatique [cs]

Denis Cornaz, Fabio Furini, Mathieu Lacroix, Enrico Malaguti, A. Ridha Mahjoub, et al.. The vertex k-cut problem. Discrete Optimization, 2019, 31, pp.8-28. ⟨10.1016/j.disopt.2018.07.003⟩. ⟨hal-02152319⟩