Separating Partition Inequalities

Baïou, Mourad; Barahona, Francisco; Mahjoub, Ali Ridha

Baïou, Mourad; Barahona, Francisco; Mahjoub, Ali Ridha (2000), Separating Partition Inequalities, Mathematics of Operations Research, 25, 2, p. 243-254. http://dx.doi.org/10.1287/moor.25.2.243.12223

Type

Article accepté pour publication ou publié

Date

2000

Journal name

Mathematics of Operations Research

Volume

Number

Publisher

Informs

Pages

243-254

Abstract (EN)

Given a graph G = (V,E) with nonnegative weights x(e) for each edge e, a partition inequality is of the form x({delta}(S1,...,Sp))≥ap+b. Here {delta}(S1,...,Sp) denotes the multicut defined by a partition S1,...,Sp of V. Partition inequalities arise as valid inequalities for optimization problems related to k-connectivity. We give a polynomial algorithm for the associated separation problem. This is based on an algorithm for finding the minimum of x({delta}(S1,...,Sp))–p that reduces to minimizing a symmetric submodular function. This is handled with the recent algorithm of Queyranne. We also survey some applications of partition inequalities.

Subjects / Keywords

k-connected subgraphs; submodular functions; separation problem; Partition inequalities