Parallel Five-cycle Counting Algorithms

Counting the frequency of subgraphs in large networks is a classic research question that reveals underlying substructures these for important applications. However, subgraph counting challenging problem, even sizes as small five, due to combinatorial explosion number possible occurrences. This article focuses on five-cycle, which an special case five-vertex and one most difficult count efficiently. We design two new parallel five-cycle algorithms prove they are work efficient achieve polylogarithmic span. Both based computing low out-degree orientations, enables computation directed two-paths three-paths, differ ways use this orientation eliminate double-counting. Additionally, we present obtaining unbiased estimates counts using graph sparsification. develop fast multicore implementations propose scheduling optimization improve their performance. Our experiments variety real-world graphs 36-core machine with two-way hyper-threading show our best exact algorithm achieves 10–46× self-relative speedup, outperforms serial benchmarks by 10–32×, previous state-of-the-art up 818×. approximate algorithm, reasonable probability parameter, 20× speedup able 9–189× faster than between 0.52% 11.77% error.