research-article

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

Authors:

Gopal Pandurangan,

Peter Robinson,

Michele ScquizzatoAuthors Info & Claims

STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

Pages 743 - 756

https://doi.org/10.1145/3055399.3055449

Published: 19 June 2017 Publication History

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.

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Cited By

Augustine JMoses WPandurangan G(2024)Awake Complexity of Distributed Minimum Spanning TreeStructural Information and Communication Complexity10.1007/978-3-031-60603-8_3(45-63)Online publication date: 23-May-2024
https://doi.org/10.1007/978-3-031-60603-8_3
Savenko BKashtalian ALysenko SSavenko O(2023)Malware Detection By Distributed Systems with Partial Centralization2023 IEEE 12th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS)10.1109/IDAACS58523.2023.10348773(265-270)Online publication date: 7-Sep-2023
https://doi.org/10.1109/IDAACS58523.2023.10348773
Wang CZhu SYu WSong LGuan X(2022)Minimum Norm Coverage Control of AUVs for Underwater Surveillance with Communication Constraints2022 American Control Conference (ACC)10.23919/ACC53348.2022.9867661(1222-1229)Online publication date: 8-Jun-2022
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Index Terms

A time- and message-optimal distributed algorithm for minimum spanning trees
1. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms

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cover image ACM Conferences

STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

June 2017

1268 pages

ISBN:9781450345286

DOI:10.1145/3055399

General Chairs:
Hamed Hatami
McGill University
,
Pierre McKenzie
Université de Montréal
,
Program Chair:
Valerie King
University of Victoria

Copyright © 2017 ACM.

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Published: 19 June 2017

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Cited By

Augustine JMoses WPandurangan G(2024)Awake Complexity of Distributed Minimum Spanning TreeStructural Information and Communication Complexity10.1007/978-3-031-60603-8_3(45-63)Online publication date: 23-May-2024
https://doi.org/10.1007/978-3-031-60603-8_3
Savenko BKashtalian ALysenko SSavenko O(2023)Malware Detection By Distributed Systems with Partial Centralization2023 IEEE 12th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS)10.1109/IDAACS58523.2023.10348773(265-270)Online publication date: 7-Sep-2023
https://doi.org/10.1109/IDAACS58523.2023.10348773
Wang CZhu SYu WSong LGuan X(2022)Minimum Norm Coverage Control of AUVs for Underwater Surveillance with Communication Constraints2022 American Control Conference (ACC)10.23919/ACC53348.2022.9867661(1222-1229)Online publication date: 8-Jun-2022
https://doi.org/10.23919/ACC53348.2022.9867661
Augustine JMoses WPandurangan GMilani AWoelfel P(2022)Brief Announcement: Distributed MST Computation in the Sleeping Model: Awake-Optimal Algorithms and Lower BoundsProceedings of the 2022 ACM Symposium on Principles of Distributed Computing10.1145/3519270.3538459(51-53)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.1145/3519270.3538459
Robinson PMarx D(2021)Being fast means being chattyProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458190(2105-2120)Online publication date: 10-Jan-2021
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Pai SPandurangan GPemmaraju SRobinson PMiller ACensor-Hillel K(2021)Can We Break Symmetry with o(m) Communication?Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing10.1145/3465084.3467909(247-257)Online publication date: 21-Jul-2021
https://dl.acm.org/doi/10.1145/3465084.3467909
Haeupler BWajc DZuzic GKhuller SVassilevska Williams V(2021)Universally-optimal distributed algorithms for known topologiesProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451081(1166-1179)Online publication date: 15-Jun-2021
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Bernstein ANanongkai D(2021)Distributed Exact Weighted All-Pairs Shortest Paths in Randomized Near-Linear TimeSIAM Journal on Computing10.1137/20M131278252:2(STOC19-112-STOC19-127)Online publication date: 23-Nov-2021
https://doi.org/10.1137/20M1312782
Saikia PKarmakar S(2021)Improved distributed approximation for Steiner tree in the CONGEST modelJournal of Parallel and Distributed Computing10.1016/j.jpdc.2021.08.004158:C(196-212)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1016/j.jpdc.2021.08.004
Kitamura NKitagawa HOtachi YIzumi T(2021)Low-congestion shortcut and graph parametersDistributed Computing10.1007/s00446-021-00401-xOnline publication date: 28-Aug-2021
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