Distributed Triangle Counting Algorithms in Simple Graph Stream

Recently, the counting algorithm of local topology structures, such as triangles, has been widely used in social network analysis, recommendation systems, user portraits and other fields. At present, one-pass streaming algorithm for counting global and local triangles has been widely studied, and most researches focus on the single-machine streaming algorithm in a 'offline+batch processing' mode. However, researches on distributed online algorithm on multiple machines are still in its infancy, and this stage has not been thoroughly studied. In this paper, we investigate the triangle counting problem in large-scale simple undirected graphs whose edges arrive as a stream. We propose two distributed online streaming algorithms to estimate the global number of triangles, which are based on the current best performance sampling-based streaming algorithm. We mainly realize the reasonable partition of the graph stream, so that each worker independently estimates the number of triangles in a subgraph of the graph stream. Experimental results show that our algorithms reduce the estimation error and are several times more accurate than state-of-the-art streaming algorithms.