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Mathematical formulations for the Balanced Vertex k-Separator Problem

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Date
2014
Dewey
Recherche opérationnelle
Sujet
graph theory
DOI
http://dx.doi.org/10.1109/CoDIT.2014.6996889
Book title
2014 International Conference on Control, Decision and Information Technologies (CoDIT)
Publisher
IEEE
Publisher city
Piscataway, NJ
Year
2014
ISBN
978-1-4799-6773-5
URI
https://basepub.dauphine.fr/handle/123456789/15619
Collections
  • LAMSADE : Publications
Metadata
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Author
Cornaz, Denis
Furini, Fabio
Lacroix, Mathieu
Malaguti, Enrico
Mahjoub, Ali Ridha
Martin, Sébastien
Type
Communication / Conférence
Item number of pages
176-181
Abstract (EN)
Given an indirected graph G = (V;E), a Vertex k-Separator is a subset of the vertex set V such that, when the separator is removed from the graph, the remaining vertices can be partitioned into k subsets that are pairwise edge-disconnected. In this paper we focus on the Balanced Vertex k-Separator Problem, i.e., the problem of finding a minimum cardinality separator such that the sizes of the resulting disconnected subsets are balanced. We present a compact Integer Linear Programming formulation for the problem, and present a polyhedral study of the associated polytope. We also present an Exponential-Size formulation, for which we derive a column generation and a branching scheme. Preliminary computational results are reported comparing the performance of the two formulations on a set of benchmark instances.

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