A Time- and message-optimal distributed algorithm for minimum spanning trees

Gopal Pandurangan, Peter Robinson, Michele Scquizzato

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

38 Scopus citations

Abstract

This paper presents a randomized (Las Vegas) distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in Õ(D + √n) time and exchanges Õ(m) messages (both with high probability), where n is the number of nodes of the network, D is the diameter, and m is the number of edges. This is the first distributed MST algorithm that matches simultaneously the time lower bound of Ω(D + √n) [Elkin, SIAM J. Comput. 2006] and the message lower bound of Ω(m) [Kutten et al., J. ACM 2015], which both apply to randomized Monte Carlo algorithms. The prior time and message lower bounds are derived using two completely different graph constructions; the existing lower bound construction that shows one lower bound does not work for the other. To complement our algorithm, we present a new lower bound graph construction for which any distributed MST algorithm requires both Ω(D + √n) rounds and Ω(m) messages.

Original languageEnglish (US)
Title of host publicationSTOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing
EditorsPierre McKenzie, Valerie King, Hamed Hatami
PublisherAssociation for Computing Machinery
Pages743-756
Number of pages14
ISBN (Electronic)9781450345286
DOIs
StatePublished - Jun 19 2017
Externally publishedYes
Event49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada
Duration: Jun 19 2017Jun 23 2017

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F128415
ISSN (Print)0737-8017

Conference

Conference49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017
Country/TerritoryCanada
CityMontreal
Period6/19/176/23/17

Keywords

  • Distributed algorithms
  • Minimum spanning trees

ASJC Scopus subject areas

  • Software

Fingerprint

Dive into the research topics of 'A Time- and message-optimal distributed algorithm for minimum spanning trees'. Together they form a unique fingerprint.

Cite this