Efficient Maximal Biclique Enumeration on Large Signed Bipartite Graphs

In this paper, we study the problem of maximal biclique enumeration on large signed bipartite graphs. Given a signed bipartite graph $G=(U,V,E,s)$ , a parameter $\theta \in [0.5, 1.0]$ , our goal is to efficiently enumerate all maximal $\theta$ -bicliques in $G$ , where a maximal $\theta$ -biclique $B(L,R)$ is a complete subgraph of $G$ with (1) the proportion of positive neighbors for each vertex in $B$ is at least $\theta$ , and (2) $B$ is not contained in another biclique $B^{\prime }$ , while $B^{\prime }$ also satisfies (1). This problem has many applications, such as biclustering for genes, recommendation of similar groups, collaboration in communities, etc. However, it is computationally challenging due to its #P-completeness. Besides, we prove that even determining the maximality of a $\theta$ -biclique is NP-hard. To the best of our knowledge, there is no efficient and scalable solution to this problem in the literature. In this paper, we first propose a branch-and-bound framework, namely ${\sf MSiBE}$ , which enumerates all maximal $\theta$ -bicliques in a depth-first manner. Then, we develop three effective optimizations to improve the performance of ${\sf MSiBE}$ . (1) The local information of each search space is utilized to enhance the pruning capacity. (2) When expanding the partial biclique, we always focus on the side with fewer candidates first, by which fruitless search branches can be skipped early. (3) We implement ${\sf MSiBE}$ with efficient array reordering techniques and set intersection strategy. To further accelerate the computation, we introduce useful graph reduction techniques. Comprehensive performance studies on 10 real datasets demonstrate that our proposals can significantly outperform the baseline methods by up to 3 orders of magnitude.