Maximum and top-k diversified biclique search at scale

Abstract

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

FPGN: follower prediction framework for infectious disease prevention

“…Thus, it can be assumed that any vertex in the biclique is closely related to all other vertices in this subgraph. However, on the one hand, biclique is an NP-hard problem that is difficult to obtain quickly by conventional ways [26,27,31]. On the other hand, biclique is too strict to provide richer structural information for the model.…”

Cohesive subgraph mining in large graphs

“…We remark that the found 𝐾 MaxBPs could have the vertices inside highly overlapped, e.g., they differ with each other only in few vertices. To solve this issue, one common practice in the literature is to find diversified cohesive subgraphs [106,107].…”