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On minimal two-edge-connected graphs

Cornaz, Denis; Magnouche, Youcef; Mahjoub, Ali Ridha (2014), On minimal two-edge-connected graphs, 2014 International Conference on Control, Decision and Information Technologies (CoDIT). Proceedings, IEEE : Piscataway, NJ, p. 251-256. 10.1109/CoDIT.2014.6996902

Type
Communication / Conférence
Date
2014
Conference title
2014 International Conference on Control, Decision and Information Technologies (CoDIT)
Conference date
2014-11
Conference city
Metz
Conference country
France
Book title
2014 International Conference on Control, Decision and Information Technologies (CoDIT). Proceedings
Publisher
IEEE
Published in
Piscataway, NJ
ISBN
978-1-4799-6773-5
Pages
251-256
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]
Magnouche, Youcef
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Mahjoub, Ali Ridha
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
Given G = (V;E) an undirected graph and a nonnegative cost function c : E → ℚ, the 2-edge connected spanning subgraph problem (TECSP for short) is to find a two-edge connected subgraph HP = (V; F) of G with minimum cost (i.e., c(F) = Σe∈F c(e) is minimum). If c(e) > 0 for all e ∈ E then every optimal solution for TECSP is an inclusionwise minimal two-edge connected subgraph. In this paper we provide preliminary results, from a polyhedral point of view, concerning the inclusionwise minimal solutions of TECSP. This problem is clearly NP-Hard. We propose an ILP formulation for the problem and study the associated polytope for the wheels. Morever, we describe some valid inequalities and propose a branch-and-cut algorithm for the problem.
Subjects / Keywords
Two-edge-connected; branch-and-cut; polyhedral approach; separation problem