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Faster Cycle Detection in the Congested Clique

Authors Keren Censor-Hillel , Tomer Even , Virginia Vassilevska Williams

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Distributed algorithms
Keywords
  • triangle detection
  • cycle detection
  • distributed computing
  • Congested Clique
  • quantum computing
  • Fast matrix multiplication
  • Fast rectangular matrix multiplication

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Abstract

We provide a fast distributed algorithm for detecting h-cycles in the Congested Clique model, whose running time decreases as the number of h-cycles in the graph increases. In undirected graphs, constant-round algorithms are known for cycles of even length. Our algorithm greatly improves upon the state of the art for odd values of h. Moreover, our running time applies also to directed graphs, in which case the improvement is for all values of h. Further, our techniques allow us to obtain a triangle detection algorithm in the quantum variant of this model, which is faster than prior work.
A key technical contribution we develop to obtain our fast cycle detection algorithm is a new algorithm for computing the product of many pairs of small matrices in parallel, which may be of independent interest.

Cite As Get BibTex

Keren Censor-Hillel, Tomer Even, and Virginia Vassilevska Williams. Faster Cycle Detection in the Congested Clique. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.12

Author Details

Keren Censor-Hillel
  • Department of Computer Science, Technion, Haifa, Israel
Tomer Even
  • Department of Computer Science, Technion, Haifa, Israel
Virginia Vassilevska Williams
  • Massachusetts Institute of Technology, Cambridge, MA, USA

Funding

  • Censor-Hillel, Keren: The research is supported in part by the Israel Science Foundation (grant 529/23).
  • Vassilevska Williams, Virginia: Supported by NSF Grant CCF-2330048, BSF Grant 2020356, and a Simons Investigator Award.

Acknowledgements

We would like to thank the anonymous reviewers for their feedback.

References

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