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A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning Trees

Authors:

Gopal Pandurangan,

Peter Robinson,

Michele ScquizzatoAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 16, Issue 1

Article No.: 13, Pages 1 - 27

https://doi.org/10.1145/3365005

Published: 15 November 2019 Publication History

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Abstract

This article 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 hop-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) [10] and the message lower bound of Ω (m) [31], 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.

References

[1]

Hagit Attiya and Jennifer Welch. 1998. Distributed Computing: Fundamentals, Simulations and Advanced Topics. McGraw-Hill, Inc.

Digital Library

[2]

Baruch Awerbuch. 1987. Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In Proceedings of the 19th ACM Symposium on Theory of Computing (STOC). 230--240.

Digital Library

[3]

Baruch Awerbuch, Oded Goldreich, David Peleg, and Ronen Vainish. 1990. A trade-off between information and communication in broadcast protocols. J. ACM 37, 2 (1990), 238--256.

Digital Library

[4]

Baruch Awerbuch and David Peleg. 1990. Sparse partitions. In Proceedings of the 31st Annual Symposium on Foundations of Computer Science (FOCS). 503--513.

Digital Library

[5]

Francis Chin and H. F. Ting. 1985. An almost linear time and O(n log n + e) messages distributed algorithm for minimum-weight spanning trees. In Proceedings of the 26th IEEE Symposium on Foundations of Computer Science (FOCS). 257--266.

[6]

Richard Cole and Uzi Vishkin. 1986. Deterministic coin tossing and accelerating cascades: micro and macro techniques for designing parallel algorithms. In Proceedings of the 18th Annual ACM Symposium on Theory of Computing (STOC). 206--219.

Digital Library

[7]

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. 2012. Distributed verification and hardness of distributed approximation. SIAM J. Comput. 41, 5 (2012), 1235--1265.

Digital Library

[8]

Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan, and Prasad Tetali. 2013. Distributed random walks. J. ACM 60, 1, Article 2 (2013).

[9]

Michael Elkin. 2006. A faster distributed protocol for constructing a minimum spanning tree. J. Comput. Syst. Sci. 72, 8 (2006), 1282--1308.

Digital Library

[10]

Michael Elkin. 2006. An unconditional lower bound on the time-approximation trade-off for the distributed minimum spanning tree problem. SIAM J. Comput. 36, 2 (2006), 433--456.

Digital Library

[11]

Michael Elkin. 2017. A simple deterministic distributed MST algorithm, with near-optimal time and message complexities. In Proceedings of the 2017 ACM Symposium on Principles of Distributed Computing (PODC). 157--163.

Digital Library

[12]

Michalis Faloutsos and Mart Molle. 2004. A linear-time optimal-message distributed algorithm for minimum spanning trees. Distributed Computing 17, 2 (2004), 151--170.

Digital Library

[13]

Eli Gafni. 1985. Improvements in the time complexity of two message-optimal election algorithms. In Proceedings of the 4th Symposium on Principles of Distributed Computing (PODC). 175--185.

Digital Library

[14]

Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. 1983. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5, 1 (1983), 66--77.

Digital Library

[15]

Juan A. Garay, Shay Kutten, and David Peleg. 1998. A sublinear time distributed algorithm for minimum-weight spanning trees. SIAM J. Comput. 27, 1 (1998), 302--316.

Digital Library

[16]

Mohsen Ghaffari and Bernhard Haeupler. 2016. Distributed algorithms for planar networks II: Low-congestion shortcuts, MST, and min-cut. In Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). 202--219.

Digital Library

[17]

Mohsen Ghaffari and Fabian Kuhn. 2018. Distributed MST and broadcast with fewer messages, and faster gossiping. In Proceedings of the 32nd International Symposium on Distributed Computing (DISC). 30:1--30:12.

[18]

Mohsen Ghaffari, Fabian Kuhn, and Hsin-Hao Su. 2017. Distributed MST and routing in almost mixing time. In Proceedings of the 2017 ACM Symposium on Principles of Distributed Computing (PODC). 131--140.

Digital Library

[19]

Robert Gmyr and Gopal Pandurangan. 2018. Time-message trade-offs in distributed algorithms. In Proceedings of the 32nd International Symposium on Distributed Computing (DISC). 32:1--32:18.

[20]

Bernhard Haeupler, D. Ellis Hershkowitz, and David Wajc. 2018. Round- and message-optimal distributed graph algorithms. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing (PODC). 119--128.

Digital Library

[21]

Bernhard Haeupler, Taisuke Izumi, and Goran Zuzic. 2016. Low-congestion shortcuts without embedding. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing (PODC). 451--460.

Digital Library

[22]

Bernhard Haeupler, Taisuke Izumi, and Goran Zuzic. 2016. Near-optimal low-congestion shortcuts on bounded parameter graphs. In Proceedings of the 30th International Symposium on Distributed Computing (DISC). 158--172.

[23]

James W. Hegeman, Gopal Pandurangan, Sriram V. Pemmaraju, Vivek B. Sardeshmukh, and Michele Scquizzato. 2015. Toward optimal bounds in the congested clique: Graph connectivity and MST. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC). 91--100.

Digital Library

[24]

Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. 2016. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. In Proceedings of the 48th ACM Symposium on Theory of Computing (STOC). 489--498.

Digital Library

[25]

Maleq Khan and Gopal Pandurangan. 2008. A fast distributed approximation algorithm for minimum spanning trees. Distributed Computing 20, 6 (2008), 391--402.

[26]

Valerie King, Shay Kutten, and Mikkel Thorup. 2015. Construction and impromptu repair of an MST in a distributed network with o(m) communication. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC). 71--80.

Digital Library

[27]

Hartmut Klauck, Danupon Nanongkai, Gopal Pandurangan, and Peter Robinson. 2015. Distributed computation of large-scale graph problems. In Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). 391--410.

Digital Library

[28]

Liah Kor, Amos Korman, and David Peleg. 2013. Tight bounds for distributed minimum-weight spanning tree verification. Theory Comput. Syst. 53, 2 (2013), 318--340.

[29]

Eyal Kushilevitz and Noam Nisan. 1997. Communication Complexity. Cambridge University Press.

Digital Library

[30]

Shay Kutten, Danupon Nanongkai, Gopal Pandurangan, and Peter Robinson. 2014. Distributed symmetry breaking in hypergraphs. In Proceedings of the 28th International Symposium on Distributed Computing (DISC). 469--483.

[31]

Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. 2015. On the complexity of universal leader election. J. ACM 62, 1, Article 7 (2015).

Digital Library

[32]

Shay Kutten and David Peleg. 1998. Fast distributed construction of small k-dominating sets and applications. J. Algorithms 28, 1 (1998), 40--66.

Digital Library

[33]

Christoph Lenzen. 2016. Lecture Notes on Theory of Distributed Systems. https://www.mpi-inf.mpg.de/fileadmin/inf/d1/teaching/winter15/tods/ToDS.pdf.

[34]

Christoph Lenzen and Boaz Patt-Shamir. 2014. Improved distributed steiner forest construction. In Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing (PODC). 262--271.

Digital Library

[35]

Nancy Lynch. 1996. Distributed Algorithms. Morgan Kaufmann Publishers.

Digital Library

[36]

Ali Mashreghi and Valerie King. 2017. Time-communication trade-offs for minimum spanning tree construction. In Proceedings of the 18th International Conference on Distributed Computing and Networking (ICDCN). Article 8.

Digital Library

[37]

Danupon Nanongkai. 2014. Distributed approximation algorithms for weighted shortest paths. In Proceedings of the 46th ACM Symposium on Theory of Computing (STOC). 565--573.

Digital Library

[38]

Danupon Nanongkai, Atish Das Sarma, and Gopal Pandurangan. 2011. A tight unconditional lower bound on distributed randomwalk computation. In Proceedings of the 30th Annual ACM Symposium on Principles of Distributed Computing (PODC). 257--266.

Digital Library

[39]

Shreyas Pai, Gopal Pandurangan, Sriram V. Pemmaraju, Talal Riaz, and Peter Robinson. 2017. Symmetry breaking in the Congest model: Time- and message-efficient algorithms for ruling sets. In Proceedings of the 31st International Symposium on Distributed Computing (DISC). 38:1--38:16.

Digital Library

[40]

Gopal Pandurangan. 2019. Distributed Network Algorithms. https://sites.google.com/site/gopalpandurangan/dna.

[41]

Gopal Pandurangan, David Peleg, and Michele Scquizzato. 2016. Message lower bounds via efficient network synchronization. In Proceedings of the 23rd International Colloquium on Structural Information and Communication Complexity (SIROCCO). 75--91.

[42]

Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. 2017. A time- and message-optimal distributed algorithm for minimum spanning trees. In Proceedings of the 49th Annual ACM Symposium on the Theory of Computing (STOC). 743--756.

Digital Library

[43]

Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. 2018. The distributed minimum spanning tree problem. Bulletin of the EATCS 125 (2018).

[44]

David Peleg. 1998. Distributed matroid basis completion via elimination upcast and distributed correction of minimum-weight spanning trees. In Proceedings of the 25th International Colloquium on Automata, Languages and Programming (ICALP). 164--175.

Digital Library

[45]

David Peleg. 2000. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics.

[46]

David Peleg and Vitaly Rubinovich. 2000. A near-tight lower bound on the time complexity of distributed minimum-weight spanning tree construction. SIAM J. Comput. 30, 5 (2000), 1427--1442.

Digital Library

[47]

Alexander A. Razborov. 1992. On the distributional complexity of disjointness. Theor. Comput. Sci. 106, 2 (1992), 385--390.

[48]

Robert Endre Tarjan. 1983. Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics.

[49]

Gerard Tel. 1994. Introduction to Distributed Algorithms. Cambridge University Press.

[50]

Andrew Chi-Chih Yao. 1977. Probabilistic computations: Toward a unified measure of complexity. In Proceedings of the 18th Annual Symposium on Foundations of Computer Science (FOCS). 222--227.

Cited By

Augustine JGilbert SKuhn FRobinson PSourav S(2022)Latency, capacity, and distributed minimum spanning treesJournal of Computer and System Sciences10.1016/j.jcss.2021.11.006126:C(1-20)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1016/j.jcss.2021.11.006
Baniata HAnaqreh AKertesz A(2021)DONS: Dynamic optimized neighbor selection for smart blockchain networksFuture Generation Computer Systems10.1016/j.future.2021.12.010Online publication date: Dec-2021
https://doi.org/10.1016/j.future.2021.12.010

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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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 16, Issue 1

Special Issue on Soda'18 and Regular Papers

January 2020

369 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3372373

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2019 ACM.

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Publication History

Published: 15 November 2019

Accepted: 01 September 2019

Revised: 01 August 2019

Received: 01 March 2018

Published in TALG Volume 16, Issue 1

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US-Israel Binational Science Foundation (BSF)
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Cited By

Augustine JGilbert SKuhn FRobinson PSourav S(2022)Latency, capacity, and distributed minimum spanning treesJournal of Computer and System Sciences10.1016/j.jcss.2021.11.006126:C(1-20)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1016/j.jcss.2021.11.006
Baniata HAnaqreh AKertesz A(2021)DONS: Dynamic optimized neighbor selection for smart blockchain networksFuture Generation Computer Systems10.1016/j.future.2021.12.010Online publication date: Dec-2021
https://doi.org/10.1016/j.future.2021.12.010

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