The vertex k-cut problem

被引：12

作者：

Cornaz, Denis ^{[1
]}

Furini, Fabio ^{[1
]}

Lacroix, Mathieu ^{[2
]}

Malaguti, Enrico ^{[3
]}

Mahjoub, A. Ridha ^{[1
]}

Martin, Sebastien ^{[4
]}

机构：

[1] Univ Paris 09, PSL, CNRS, LAMSADE UMR 7243, F-75775 Paris 16, France

[2] Univ Paris 13, Sorbonne Paris Cite, LIPN, CNRS,UMR 7030, Ave JB Clement, F-93430 Villetaneuse, France

[3] Univ Bologna, DEI, Viale Risorgimento 2, I-40136 Bologna, Italy

[4] Univ Lorraine, LCOMS, F-57045 Metz, France

来源：

DISCRETE OPTIMIZATION | 2019年 / 31卷

关键词：

Vertex cut; Mixed-integer programming models; Branch and Price; Exact algorithms; SEPARATOR PROBLEM; ALGORITHM; COMPLEXITY;

D O I：

10.1016/j.disopt.2018.07.003

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Given an undirected graph G = (V, E), a vertex k-cut of G is a vertex subset of V the removing of which disconnects the graph in at least k components. Given a graph G and an integer k >= 2, the vertex k-cut problem consists in finding a vertex k-cut of G of 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. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：8 / 28

页数：21

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