Deterministic PRAM approximate shortest paths in polylogarithmic time and slightly super-linear work

Michael Elkin, Shaked Matar

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

Abstract

We study a (1+ϵ)-approximate single-source shortest paths (henceforth, (1+ϵ)-SSSP) in n-vertex undirected, weighted graphs in the parallel (PRAM) model of computation. A randomized algorithm with polylogarithmic time and slightly super-linear work Õ(|E|•n^ρ), for an arbitrarily small ρ>0, was given by Cohen (10) more than 25 years ago. Exciting progress on this problem was achieved in recent years (4, 17, 19, 35), culminating in randomized polylogarithmic time and Õ(|E|) work. However, the question of whether there exists a deterministic counterpart of Cohen's algorithm remained wide open. In the current paper we devise the first deterministic polylogarithmic-time algorithm for this fundamental problem, with work Õ(|E|•n^ρ), for an arbitrarily small ρ>0. This result is based on the first efficient deterministic parallel algorithm for building hopsets, which we devise in this paper.

Original languageEnglish
Title of host publicationSPAA 2021 - Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages198-207
Number of pages10
ISBN (Electronic)9781450380706
DOIs
StatePublished - 6 Jul 2021
Event33rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2021 - Virtual, Online, United States
Duration: 6 Jul 20218 Jul 2021

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference33rd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2021
Country/TerritoryUnited States
CityVirtual, Online
Period6/07/218/07/21

Keywords

  • Approximate single source shortest paths
  • Deterministic
  • Hopsets
  • Pram

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