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Parallel Five-Cycle Counting Algorithms

Authors Louisa Ruixue Huang, Jessica Shi, Julian Shun

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Subject Classification

ACM Subject Classification
  • Theory of computation → Shared memory algorithms
  • Theory of computation → Graph algorithms analysis
  • Computing methodologies → Shared memory algorithms
Keywords
  • Cycle counting
  • parallel algorithms
  • graph algorithms

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Abstract

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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.SEA.2021.2

Author Details

Louisa Ruixue Huang
  • MIT, CSAIL, Cambridge, MA, USA
Jessica Shi
  • MIT, CSAIL, Cambridge, MA, USA
Julian Shun
  • MIT, CSAIL, Cambridge, MA, USA

Funding

This research was supported by NSF Graduate Research Fellowship #1122374, DOE Early Career Award #DESC0018947, NSF CAREER Award #CCF-1845763, Google Faculty Research Award, DARPA SDH Award #HR0011-18-3-0007, and Applications Driving Architectures (ADA) Research Center, a JUMP Center co-sponsored by SRC and DARPA.

Supplementary Materials

References

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