Fast approximate shortest paths in the congested clique

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We design fast deterministic algorithms for distance computation in the CONGESTED CLIQUE model. Our key contributions include: A (2+)-approximation for all-pairs shortest paths problem in O(log2n / ) 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+)-approximation for multi-source shortest paths problem from O(n) sources in O(log2 n / ) 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 (n1/6) rounds.

Original languageEnglish
Title of host publicationPODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages74-83
Number of pages10
ISBN (Electronic)9781450362177
DOIs
StatePublished - 16 Jul 2019
Externally publishedYes
Event38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada
Duration: 29 Jul 20192 Aug 2019

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference38th ACM Symposium on Principles of Distributed Computing, PODC 2019
Country/TerritoryCanada
CityToronto
Period29/07/192/08/19

Bibliographical note

Publisher Copyright:
© 2019 ACM.

Keywords

  • All-pairs shortest paths
  • Congested clique
  • Diameter
  • Distributed computing
  • Hopsets
  • Matrix multiplication
  • Single-source shortest paths
  • approximation algorithms

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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