Identifying similar-bicliques in bipartite graphs

Abstract

Bipartite graphs have been widely used to model the relationship between entities of different types, where vertices are partitioned into two disjoint sets/sides. Finding dense subgraphs in a bipartite graph is of great significance and encompasses many applications. However, none of the existing dense bipartite subgraph models consider similarity between vertices from the same side, and as a result, the identified results may include vertices that are not similar to each other. In this work, we formulate the notion of similar-biclique which is a special kind of biclique where all vertices from a designated side are similar to each other and aim to enumerate all similar-bicliques. The naive approach of first enumerating all maximal bicliques and then extracting all maximal similar-bicliques from them is inefficient, as enumerating maximal bicliques is already time consuming. We propose a backtracking algorithm MSBE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{MSBE}$$\\end{document} to directly enumerate maximal similar-bicliques and power it by vertex reduction and optimization techniques. In addition, we design a novel index structure to speed up a time-critical operation of MSBE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{MSBE}$$\\end{document}, as well as to speed up vertex reduction. Efficient index construction algorithms are developed. To handle dynamic graph updates, we also propose algorithms and optimization techniques for maintaining our index. Finally, we parallelize our index construction algorithms to exploit multiple CPU cores. Extensive experiments on 17 bipartite graphs as well as case studies are conducted to demonstrate the effectiveness and efficiency of our model and algorithms.