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Finding Maximum Edge Bicliques in Convex Bipartite Graphs

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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 v∈A, 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(nα(n)) and O(n) time, respectively, where n=min (|A|,|B|) and α(n) is the slowly growing inverse of the Ackermann function.

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Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Doron Nussbaum, Jörg-Rüdiger Sack & Hamid Zarrabi-Zadeh

  2. Program in Molecular Structure and Function, Hospital for Sick Children, 555 University Avenue, Toronto, ON, M5G 1X8, Canada

    Shuye Pu

  3. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Takeaki Uno

  4. Department of Computer Engineering, Sharif University of Technology, Tehran, Iran

    Hamid Zarrabi-Zadeh

Authors
  1. Doron Nussbaum
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  2. Shuye Pu
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  3. Jörg-Rüdiger Sack
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  4. Takeaki Uno
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  5. Hamid Zarrabi-Zadeh
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Corresponding author

Correspondence to Hamid Zarrabi-Zadeh.

Additional information

Research supported by NSERC and SUN Microsystems. A preliminary version of this work appeared in the 16th Annual International Computing and Combinatorics Conference (COCOON 2010).

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Nussbaum, D., Pu, S., Sack, JR. et al. Finding Maximum Edge Bicliques in Convex Bipartite Graphs. Algorithmica 64, 311–325 (2012). https://doi.org/10.1007/s00453-010-9486-x

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  • DOI: https://doi.org/10.1007/s00453-010-9486-x

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