Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Randomized algorithms
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On the closest string and substring problems
Journal of the ACM (JACM)
A lock-and-key model for protein--protein interactions
Bioinformatics
Finding biclusters by random projections
Theoretical Computer Science
A Chernoff bound for random walks on expander graphs
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Quasi-bicliques: Complexity and Binding Pairs
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Modeling Protein Interacting Groups by Quasi-Bicliques: Complexity, Algorithm, and Application
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Mining biological interaction networks using weighted quasi-bicliques
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
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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 Xopt of X and a subset Yopt of Y such that any vertex x ∈ Xopt is incident to at least (1 - δ)|Yopt| vertices in Yopt, any vertex y ∈ Yopt is incident to at least (1 - δ)|Xopt| vertices in Xopt and |Xopt| + |Yopt| is maximized. The problem was proved to be NP-hard [2]. We design a polynomial time approximation scheme to give a quasi-biclique (Xa, Ya) for Xa ⊆ X and Ya ⊆ Y with |Xa| ≥ (1 - ε)|Xopt| and |Ya| ≥ (1 -ε)|Ya| such that any vertex x ∈ Xa is incident to at least (1 - δ - ε)|Ya| vertices in Ya and any vertex y ∈ Ya is incident to at least (1 - δ - ε)|Xa| vertices in Xa for any ε 0, where Xopt and Yopt form the optimal solution.