A Fast Parallel Algorithm for Counting Triangles in Graphs using Dynamic Load Balancing

Abstract—Finding the number of triangles in a graph (net-work) is an important problem in graph analysis. The number of triangles also has important applications in graph mining. Big graphs emerging from numerous application areas pose a significant challenge for the analysis and mining since these graphs consist of millions, or even billions, of nodes and edges. Graphs of such scale necessitate the development of efficient parallel algorithms. Existing distributed memory parallel al-gorithms for counting exact triangles are either Map-Reduce or message passing interface (MPI) based. Map-Reduce based algorithms generate prohibitively large intermediate data and do not demonstrate reasonably good runtime efficiency. The MPI based algorithms offer fast computation of the number of triangles. However, the partitioning and load balancing schemes these algorithms employ are static in nature – the partitions are precomputed based on some estimations. In this paper, we present an efficient MPI-based parallel algorithm for counting triangles in large graph. We consider the case where the main memory of each compute node is large enough to contain the entire graph. We observe that for such a case, computation load can be balanced dynamically and present a dynamic load balancing scheme which improves the performance of the algorithm significantly. Our algorithm demonstrates very good speedups and scales to a large number of processors. The algorithm computes the exact number of triangles in a network with 1 billion edges in 2 minutes with only 100 processors. Our results demonstrate that the algorithm is significantly faster than the related algorithms with static partitioning. In fact, for the real-world networks we experimented on, our algorithm achieves at least 2 times runtime efficiency over the fastest algorithm with static load balancing. Keywords-triangle-counting; parallel algorithms; large graphs; graph mining; social networks. I