Fast distributed algorithms for connectivity and MST in large graphs

Gopal Pandurangan, Peter Robinson, Michele Scquizzato

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Scopus citations

Abstract

Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where k ≥ 2 machines jointly perform computations on graphs with n nodes (typically, n > k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. Our main result is an (almost) optimal distributed randomized algorithm for graph connectivity. Our algorithm runs in Õ(n/k) rounds (Õ notation hides a polylog(n) factor and an additive polylog(n) term). This improves over the best previously known bound of Õ(n/k)[Klauck et al., SODA 2015], and is optimal (up to a polylogarithmic factor) in view of an existing lower bound of Ω(n/k2). Our improved algorithm uses a bunch of techniques, including linear graph sketching, that prove useful in the design of efficient distributed graph algorithms. We then present fast randomized algorithms for computing minimum spanning trees, (approximate) min-cuts, and for many graph verification problems. All these algorithms take Õ(n/k2) rounds, and are optimal up to polylogarithmic factors. We also show an almost matching lower bound of Ω(n/k2) for many graph verification problems using lower bounds in random-partition communication complexity.

Original languageEnglish (US)
Title of host publicationSPAA 2016 - Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages429-438
Number of pages10
ISBN (Electronic)9781450342100
DOIs
StatePublished - Jul 11 2016
Externally publishedYes
Event28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016 - Pacific Grove, United States
Duration: Jul 11 2016Jul 13 2016

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures
Volume11-13-July-2016

Conference

Conference28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016
Country/TerritoryUnited States
CityPacific Grove
Period7/11/167/13/16

Keywords

  • Distributed graph algorithms
  • Graph connectivity
  • Graph sketching
  • Massive graphs
  • Minimum spanning trees

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

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