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Near optimal solutions for maximum quasi-bicliques

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Abstract

The maximum quasi-biclique problem has been proposed for finding interacting protein group pairs from large protein-protein interaction (PPI) networks. The problem is defined as follows:

The Maximum Quasi-biclique Problem: Given a bipartite graph G=(X∪Y,E) and a number 0<δ≤0.5, find a subset X opt of X and a subset Y opt of Y such that any vertex x∈X opt is incident to at least (1−δ)|Y opt | vertices in Y opt , any vertex y∈Y opt is incident to at least (1−δ)|X opt | vertices in X opt and |X opt |+|Y opt | is maximized.

The problem was proved to be NP-hard. We design a polynomial time approximation scheme to give a quasi-biclique X′⊆X and Y′⊆Y with |X′|+|Y′|≥(1−ε)(|X opt |+|Y opt |) such that any vertex x∈X′ is incident to at least (1−δ−ε)|Y′| vertices in Y′ and any vertex y∈Y′ is incident to at least (1−δ−ε)|X′| vertices in X′ for any ε>0, where X opt and Y opt form the optimal solution.

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Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

    Lusheng Wang

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  1. Lusheng Wang
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Correspondence to Lusheng Wang.

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Wang, L. Near optimal solutions for maximum quasi-bicliques. J Comb Optim 25, 481–497 (2013). https://doi.org/10.1007/s10878-011-9392-4

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  • DOI: https://doi.org/10.1007/s10878-011-9392-4

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