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The vertex k-cut problem

Cornaz, Denis; Furini, Fabio; Lacroix, Mathieu; Malaguti, Enrico; Mahjoub, Ali Ridha; Martin, Sébastien (2019), The vertex k-cut problem, Discrete Optimization, 31, p. 8-28. 10.1016/j.disopt.2018.07.003

Type
Article accepté pour publication ou publié
Date
2019
Journal name
Discrete Optimization
Volume
31
Publisher
Elsevier
Pages
8-28
Publication identifier
Metadata
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Author(s)
Cornaz, Denis
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Furini, Fabio
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lacroix, Mathieu cc
Laboratoire d'Informatique de Paris-Nord [LIPN]
Malaguti, Enrico
D.E.I. - University of Bologna.
Mahjoub, Ali Ridha
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Martin, Sébastien cc
Laboratoire de Conception, Optimisation et Modélisation des Systèmes [LCOMS]
Abstract (EN)
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.
Subjects / Keywords
Vertex cut; Mixed-integer programming models; Branch and Price; Exact algorithms