Consensus algorithms for the generation of all maximal bicliques

• Published in: Discrete Applied Mathematics Vol. 145; no. 1; pp. 11 - 21
• Main Authors: Alexe, Gabriela, Alexe, Sorin, Crama, Yves, Foldes, Stephan, Hammer, Peter L., Simeone, Bruno
• Format: Journal Article Conference Proceeding Web Resource
• Language: English
• Published: Lausanne Elsevier B.V 30.12.2004; Amsterdam Elsevier; New York, NY Elsevier Science Bv
• Subjects: Algorithmic graph theory; Algorithmics. Computability. Computer arithmetics; Applied sciences; Biclique; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Consensus-type algorithm; Exact sciences and technology; General logic; Graph theory; Incremental polynomial enumeration; Information retrieval. Graph; Logic and foundations; Mathematical logic, foundations, set theory; Mathematics; Mathématiques; Maximal complete bipartite subgraph; Physical, chemical, mathematical & earth Sciences; Physique, chimie, mathématiques & sciences de la terre; Sciences and techniques of general use; Theoretical computing; Maximal complete bipartite subgraph; Algorithmic graph theory; Incremental polynomial enumeration; Biclique; Consensus-type algorithm; Propositional logic; Maxumum complete bipartite subgraph; Computer theory; Consensus type algorithm; Graph theory; Combinatorics; Complexity
• ISSN: 0166-218X; 1872-6771; 1872-6771
• DOI: 10.1016/j.dam.2003.09.004

We describe a new algorithm for generating all maximal bicliques (i.e. complete bipartite, not necessarily induced subgraphs) of a graph. The algorithm is inspired by, and is quite similar to, the consensus method used in propositional logic. We show that some variants of the algorithm are totally polynomial, and even incrementally polynomial. The total complexity of the most efficient variant of the algorithms presented here is polynomial in the input size, and only linear in the output size. Computational experiments demonstrate its high efficiency on randomly generated graphs with up to 2000 vertices and 20,000 edges.