Generating bicliques of a graph in lexicographic order

  • Authors:

  • Vânia M. F. Dias;Celina M. H. de Figueiredo;Jayme L. Szwarcfiter

  • Affiliations:

  • Universidade Federal do Rio de Janeiro, COPPE, Caixa Postal 68530, 21945-970 Rio de Janeiro, Brazil;Universidade Federal do Rio de Janeiro, IM and COPPE, Caixa Postal 68530, 21945-970 Rio de Janeiro, Brazil;Universidade Federal do Rio de Janeiro, IM, COPPE, and NCE, Caixa Postal 68511, 21945-970 Rio de Janeiro, Brazil

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2005

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Abstract

An independent set of a graph is a subset of pairwise non-adjacent vertices. A complete bipartite set B is a subset of vertices admitting a bipartition B = X ∪ Y, such that both X and Y are independent sets, and all vertices of X are adjacent to those of Y. If both X, Y ≠ 0, then B is called proper. A biclique is a maximal proper complete bipartite set of a graph. We present an algorithm that generates all bicliques of a graph in lexicographic order, with polynomial-time delay between the output of two successive bicliques. We also show that there is no polynomial-time delay algorithm for generating all bicliques in reverse lexicographic order, unless P = NP. The methods are based on those by Johnson, Papadimitriou and Yannakakis, in the solution of these two problems for independent sets, instead of bicliques.