Efficient Maximum Signed Biclique Identification

Maximum biclique identification, which aims to find the biclique with the largest size, can find a wide spectrum of applications in different domains, such as E-Commerce, healthcare and bioinformatics. However, the previous studies mainly focus on unsigned bipartite graphs. The signed information naturally exists in real applications, such as like and dislike. The neglect of signed information may fail to discover the inherent properties of networks. In this paper, we propose a novel model, named signed (k,l)-biclique (SKLB), by enforcing constraints over the number of positive and negative connections. Specifically, given a signed bipartite graph and two positive integers k,l, SKLB is a biclique, where each vertex has no less than k positive neighbors and no more than l negative neighbors. We prove the problem of finding the maximum signed (k,l)-biclique (MaxSKLB) is NP-hard. Moreover, we show that the problem is still NP-hard, even if the input graph is a biclique itself. A baseline algorithm is first presented through biclique enumeration, which tries to find the MaxSKLB for each encountered biclique and return the largest one. However, considering that the extraction of MaxSKLB from a biclique is still NP-hard, a greedy strategy is developed to accelerate the processing with competitive result. Furthermore, to efficiently handle large graphs, we optimize the algorithm from different perspectives, including unnecessary search branches and unpromising vertices filtering. Finally, comprehensive experiments are conducted over 10 graphs to validate the efficiency and effectiveness of proposed techniques and model.