Quasi-bicliques: Complexity and Binding Pairs

Protein-protein interactions (PPIs) are one of the most important mechanisms in cellular processes. To model protein interaction sites, recent studies have suggested to find interacting protein group pairs from large PPI networks at the first step, and then to search conserved motifs within the protein groups to form interacting motif pairs. To consider noise effect and incompleteness of biological data, we propose to use quasi-bicliques for finding interacting protein group pairs. We investigate two new problems which arise from finding interacting protein group pairs: the maximum vertex quasi-biclique problem and the maximum balanced quasi-biclique problem. We prove that both problems are NP-hard. This is a surprising result as the widely known maximum vertex biclique problem is polynomial time solvable [16]. We then propose a heuristic algorithm which uses the greedy method to find the quasi-bicliques from PPI networks. Our experiment results on real data show that this algorithm has a better performance than a benchmark algorithm for identifying highly matched BLOCKS and PRINTS motifs.