Consensus algorithms for the generation of all maximal bicliques

  • Authors:

  • Gabriela Alexe;Sorin Alexe;Yves Crama;Stephan Foldes;Peter L. Hammer;Bruno Simeone

  • Affiliations:

  • RUTCOR, Rutgers, the State University of New Jersey, 640 Bartholomew Road, Piscataway, NJ;RUTCOR, Rutgers, the State University of New Jersey, 640 Bartholomew Road, Piscataway, NJ;Ecole d' Administration des Affaires, University of Liège, Boulevard du Rectorat 7 (B31), 4000 Liège, Belgium;Department of Mathematics, Tempere University of Technology, Tempere-Hervanta, Finland;RUTCOR, Rutgers, the State University of New Jersey, 640 Bartholomew Road, Piscataway, NJ;Department of Statistics, "La Sapienza" University, Piazzale Aldo Moro 5, 00185, Rome, Italy

  • Venue:
  • Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
  • Year:
  • 2004

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Abstract

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.