Maximum and top-k diversified biclique search at scale

Abstract Maximum biclique search, which finds the with maximum number of edges in a bipartite graph, is fundamental problem wide spectrum applications different domains, such as E-Commerce, social analysis, web services, and bioinformatics. Unfortunately, due to difficulty graph theory, no practical solution has been proposed solve issue large-scale real-world datasets. Existing techniques for clique search on general cannot be applied because objective two-dimensional, i.e., we have consider size both parts simultaneously. In this paper, divide into several subproblems each specified using two parameters. These are derived progressive manner, subproblem, can restrict very small part original graph. We prove that logarithmic enough guarantee algorithm correctness. To minimize computational cost, show how reduce significantly subproblem while preserving satisfying certain constraints by exploring properties one-hop two-hop neighbors vertex. Furthermore, study diversified top- k aims find maximal bicliques cover most total. The basic idea repeatedly remove it from times. design an efficient considers share computation cost among results, based deriving same results. further propose optimizations accelerate pruning space constraint refining candidates lazy manner. use real datasets various application one contains over 300 million vertices 1.3 billion edges, demonstrate high efficiency scalability our solution. It reported 50% improvement recall achieved after applying method Alibaba Group identify fraudulent transactions their e-commerce networks. This demonstrates usefulness practice.