Fast approximate shortest paths in the congested clique

Keren Censor-Hillel, Michal Dory, Janne H. Korhonen, Dean Leitersdorf

Research output: Contribution to journalArticlepeer-review


We design fast deterministic algorithms for distance computation in the Congested Clique model. Our key contributions include:A (2 + ϵ) -approximation for all-pairs shortest paths in O(log 2n/ ϵ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model.A (1 + ϵ) -approximation for multi-source shortest paths from O(n) sources in O(log 2n/ ϵ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in O~ (n1 / 6) rounds.

Original languageEnglish
Pages (from-to)463-487
Number of pages25
JournalDistributed Computing
Issue number6
StatePublished - Dec 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020, The Author(s).


  • All-pairs shortest paths
  • Congested clique model
  • Distributed computing
  • Hopsets
  • Matrix multiplication

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computational Theory and Mathematics


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