On co-bicliques

Cornaz, Denis

doi:10.1051/ro:2007020

On co-bicliques

Cornaz, Denis

RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 295-304.

Résumé

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 $F \subseteq E$ is an independent of $G$ if there is a co-biclique $B$ such that $F \subseteq B$ , 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 $x \in ℚ_{+}^{E}$ . Based on this, we obtain a branch-and-cut algorithm for the maximum co-biclique problem which is, given a weight vector $w \in ℚ_{+}^{E}$ , to find a co-biclique $B$ of $G$ maximizing $w (B) = \sum_{e \in B} w_{e}$ .

DOI : 10.1051/ro:2007020

Classification : 05C15, 90C09
Mots-clés : co-bicyclique, signed graph, branch-and-cut

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     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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     publisher = {EDP-Sciences},
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Cornaz, Denis. On co-bicliques. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 295-304. doi : 10.1051/ro:2007020. http://www.numdam.org/articles/10.1051/ro:2007020/

Bibliographie
Cité par

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