Distributed, Shared-Memory Parallel Triangle Counting

Triangles are the most basic non-trivial subgraphs. Triangle counting is used in a number of different applications, including social network mining, cyber security, and spam detection. In general, triangle counting algorithms are readily parallelizable, but when implemented in distributed, shared-memory, their performance is poor due to high communication, imbalance of work, and the difficulty of exploiting locality available in shared memory. In this paper, we discuss four different (but related) triangle counting algorithms and how their performance can be improved in distributed, shared-memory by reducing in-node load imbalance, improving cache utilization, minimizing network overhead, and minimizing algorithmic work. We generalize the four different triangle counting algorithms into a common framework and show that for all four algorithms the in-node load imbalance can be minimized while utilizing caches by partitioning work into blocks of vertices, the network overhead can be minimized by aggregation of blocks of work, and algorithm work can be reduced by partitioning vertex neighbors by degree. We experimentally evaluate the weak and the strong scaling performance of the proposed algorithms with two types of synthetic graph inputs and three real-world graph inputs. We also compare the performance of our implementations with the distributed, shared-memory triangle counting algorithms available in PowerGraph-GraphLab and show that our proposed algorithms outperform those algorithms, both in terms of space and time.