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On co-bicliques

Published online by Cambridge University Press:  21 August 2007

Denis Cornaz
Denis Cornaz*
Affiliation:
Équipe Combinatoire, UFR 921, Case 189, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05 France; cornaz@math.jussieu.fr
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Abstract

A co-biclique of a simple undirected graph G = (V,E) is the edge-set of two disjoint complete subgraphs of G. (A co-biclique is the complement of a biclique.) A subset F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C is an independent.) It is showed that a minimum-cost dependent set of G can be determined in polynomial time for any nonnegative cost vector $x\in \mathbb Q_+^E$. Based on this, we obtain a branch-and-cut algorithm for the maximum co-biclique problem which is, given a weight vector $w\in \mathbb Q_+^E$, to find a co-biclique B of G maximizing w(B) = ∑e∈B we.

Keywords

Co-bicycliquesigned graphbranch-and-cut
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 3: Journées Polyèdres et Optimisation Combinatoire , July 2007 , pp. 295 - 304
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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References

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