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Algorithmica

, Volume 64, Issue 2, pp 311–325 | Cite as

Finding Maximum Edge Bicliques in Convex Bipartite Graphs

  • Doron Nussbaum
  • Shuye Pu
  • Jörg-Rüdiger Sack
  • Takeaki Uno
  • Hamid Zarrabi-Zadeh
Article

Abstract

A bipartite graph G=(A,B,E) is convex on B if there exists an ordering of the vertices of B such that for any vertex vA, vertices adjacent to v are consecutive in B. A complete bipartite subgraph of a graph G is called a biclique of G. Motivated by an application to analyzing DNA microarray data, we study the problem of finding maximum edge bicliques in convex bipartite graphs. Given a bipartite graph G=(A,B,E) which is convex on B, we present a new algorithm that computes a maximum edge biclique of G in O(nlog 3 nlog log n) time and O(n) space, where n=|A|. This improves the current O(n 2) time bound available for the problem. We also show that for two special subclasses of convex bipartite graphs, namely for biconvex graphs and bipartite permutation graphs, a maximum edge biclique can be computed in O((n)) and O(n) time, respectively, where n=min (|A|,|B|) and α(n) is the slowly growing inverse of the Ackermann function.

Keywords

Bicliques Convex bipartite graphs Biconvex graphs Bipartite permutation graphs 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Doron Nussbaum
    • 1
  • Shuye Pu
    • 2
  • Jörg-Rüdiger Sack
    • 1
  • Takeaki Uno
    • 3
  • Hamid Zarrabi-Zadeh
    • 1
    • 4
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Program in Molecular Structure and FunctionHospital for Sick ChildrenTorontoCanada
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.Department of Computer EngineeringSharif University of TechnologyTehranIran

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