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 [2]. We design a polynomial time approximation scheme to give a quasi-biclique (X a , Y a ) for X a ⊆ X and Y a ⊆ Y with |X a | ≥ (1 − ε)|X opt | and |Y a | ≥ (1 − ε)|Y opt | such that any vertex x ∈ X a is incident to at least (1 − δ − ε)|Y a | vertices in Y a and any vertex y ∈ Y a is incident to at least (1 − δ − ε)|X A | vertices in X a for any ε> 0, where X opt and Y opt form the optimal solution.
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Wang, L. (2010). Near Optimal Solutions for Maximum Quasi-bicliques. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_44
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DOI: https://doi.org/10.1007/978-3-642-14031-0_44
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