Issue |
RAIRO-Oper. Res.
Volume 41, Number 3, July-September 2007
Journées Polyèdres et Optimisation Combinatoire
|
|
---|---|---|
Page(s) | 295 - 304 | |
DOI | https://doi.org/10.1051/ro:2007020 | |
Published online | 21 August 2007 |
On co-bicliques
Équipe Combinatoire, UFR 921, Case 189,
Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris
Cedex 05 France; cornaz@math.jussieu.fr
Received:
4
December
2006
Accepted:
21
December
2006
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 . Based on this, we obtain a branch-and-cut algorithm for the maximum co-biclique problem which is, given a weight vector
, to find a co-biclique B of G maximizing w(B) = ∑e∈B we.
Mathematics Subject Classification: 05C15 / 90C09
Key words: Co-bicyclique / signed graph / branch-and-cut
© EDP Sciences, ROADEF, SMAI, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.