LAUSR

Tip decomposition has a pivotal role in mining cohesive subgraphs in bipartite graphs by computing the tip number of each vertex in accordance with the non-trivial motif butterfly ((2,2)-biclique). It has been a popular research topic with applications in document clustering, spam group detection, and analysis of affiliation networks. In such applications, the graphs are not only large, but they evolve quickly with new edges being continuously added/deleted. While existing centralized techniques could solve the tip decomposition problem for static bipartite graphs, they are not efficient for maintaining the tip numbers of vertices on large-scale graphs. In this paper, we study butterfly analysis problems on bipartite graphs in a distributed environment with the vertex-centric model. We first extend a centralized butterfly counting algorithm to a distributed version, called DBCA. An ingenious message aggregation strategy is designed to reduce massive redundant messaging and avoid the memory overflow problem while processing large-scale graphs. Based on the results of DBCA, we develop a distributed tip decomposition algorithm (DTDA) to get the tip number of each vertex in parallel. Finally, to maintain the tip numbers of vertices efficiently while graphs evolve over time, we explore a distributed tip maintenance algorithm (DTMA) along with a novel task-split strategy. Specifically, for an updated edge (insertion/deletion), several sub-tasks will be generated in line with the topology structure of the original bipartite graph. To our best knowledge, this is the first study to process the butterfly analysis problems in a distributed environment. In addition, comprehensive experiments have been conducted on real-world bipartite graphs. The experiment results demonstrate that our proposed algorithms are efficient and scalable.