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Parallel Five-Cycle Counting Algorithms

Authors: Louisa Ruixue Huang, Jessica Shi, and Julian Shun

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Counting the frequency of subgraphs in large networks is a classic research question that reveals the underlying substructures of these networks for important applications. However, subgraph counting is a challenging problem, even for subgraph sizes as small as five, due to the combinatorial explosion in the number of possible occurrences. This paper focuses on the five-cycle, which is an important special case of five-vertex subgraph counting and one of the most difficult to count efficiently. We design two new parallel five-cycle counting algorithms and prove that they are work-efficient and achieve polylogarithmic span. Both algorithms are based on computing low out-degree orientations, which enables the efficient computation of directed two-paths and three-paths, and the algorithms differ in the ways in which they use this orientation to eliminate double-counting. We develop fast multicore implementations of the algorithms and propose a work scheduling optimization to improve their performance. Our experiments on a variety of real-world graphs using a 36-core machine with two-way hyper-threading show that our algorithms achieves 10-46x self-relative speed-up, outperform our serial benchmarks by 10-32x, and outperform the previous state-of-the-art serial algorithm by up to 818x.

Cite as

Louisa Ruixue Huang, Jessica Shi, and Julian Shun. Parallel Five-Cycle Counting Algorithms. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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  author =	{Huang, Louisa Ruixue and Shi, Jessica and Shun, Julian},
  title =	{{Parallel Five-Cycle Counting Algorithms}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{2:1--2:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.2},
  URN =		{urn:nbn:de:0030-drops-137749},
  doi =		{10.4230/LIPIcs.SEA.2021.2},
  annote =	{Keywords: Cycle counting, parallel algorithms, graph algorithms}
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