Maximum and top-k diversified biclique search at scale View Full Text


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Article Info

DATE

2022-04-18

AUTHORS

Bingqing Lyu, Lu Qin, Xuemin Lin, Ying Zhang, Zhengping Qian, Jingren Zhou

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. More... »

PAGES

1-25

References to SciGraph publications

  • 2014-04-15. On finding bicliques in bipartite graphs: a novel algorithm and its application to the integration of diverse biological data types in BMC BIOINFORMATICS
  • 2005. A Correspondence Between Maximal Complete Bipartite Subgraphs and Closed Patterns in KNOWLEDGE DISCOVERY IN DATABASES: PKDD 2005
  • 2003-06-18. An Efficient Branch-and-Bound Algorithm for Finding a Maximum Clique in DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
  • 2016-05-27. A Much Faster Branch-and-Bound Algorithm for Finding a Maximum Clique in FRONTIERS IN ALGORITHMICS
  • 2013-05-16. Speeding up branch and bound algorithms for solving the maximum clique problem in JOURNAL OF GLOBAL OPTIMIZATION
  • 2006-07-06. An Efficient Branch-and-bound Algorithm for Finding a Maximum Clique with Computational Experiments in JOURNAL OF GLOBAL OPTIMIZATION
  • 2014. An Exact Branch and Bound Algorithm with Symmetry Breaking for the Maximum Balanced Induced Biclique Problem in INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING
  • 2016-03-15. Bicliques in Graphs with Correlated Edges: From Artificial to Biological Networks in APPLICATIONS OF EVOLUTIONARY COMPUTATION
  • 2006. Efficient Mining of Large Maximal Bicliques in DATA WAREHOUSING AND KNOWLEDGE DISCOVERY
  • 2015-10-30. Diversified top-k clique search in THE VLDB JOURNAL
  • 2010. A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique in WALCOM: ALGORITHMS AND COMPUTATION
  • 2019-10-26. Efficient community discovery with user engagement and similarity in THE VLDB JOURNAL
  • 2013. Collusion Detection in Online Rating Systems in WEB TECHNOLOGIES AND APPLICATIONS
  • 2004. New Algorithms for Enumerating All Maximal Cliques in ALGORITHM THEORY - SWAT 2004
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