research-article

Open access

Time-communication trade-offs for minimum spanning tree construction

Authors:

Valerie KingAuthors Info & Claims

ICDCN '17: Proceedings of the 18th International Conference on Distributed Computing and Networking

Article No.: 8, Pages 1 - 10

https://doi.org/10.1145/3007748.3007775

Published: 05 January 2017 Publication History

Abstract

This paper concerns the problem of constructing a minimum spanning tree (MST) in a synchronous distributed network with n nodes, where each node knows only the identities of itself and its neighbors. We assume the CONGEST model where messages are of size O(log n) bits. Spanning tree construction was long believed to require an amount of communication linear in the number of edges. In 2015, King, Kutten and Thorup presented a Monte Carlo algorithm which broke this communication bound. In particular it showed that an MST could be constructed with time and message complexity O(n log2 n/log log n), independent of the number of edges.

Here we give trade-offs between time and communication. Our Monte Carlo algorithm runs in O(n/ϵ) time and O(n1+ϵ/ϵ log log n) messages for any 1 > ϵ ≥ log log n log n. For the spanning tree problem, we show a time bound of O(n) and a communication bound of O(n log n log log n) messages. We also provide the first algorithm that constructs an MST in time proportional to the diameter of the MST up to a logarithmic factor with o(m) communication.

References

[1]

[Awe87] Baruch Awerbuch. Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In Proceedings of the nineteenth annual ACM symposium on Theory of computing, pages 230--240. ACM, 1987.

Digital Library

[2]

[CT85] F Chin and HF Ting. An almost linear time and o (nlogn+ e) messages distributed algorithm for minimum-weight spanning trees. In Foundations of Computer Science, 1985., 26th Annual Symposium on, pages 257--266. IEEE, 1985.

Digital Library

[3]

[Elk04] Michael Elkin. A faster distributed protocol for constructing a minimum spanning tree. In Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pages 359--368. Society for Industrial and Applied Mathematics, 2004.

Digital Library

[4]

[Elk06] Michael Elkin. An unconditional lower bound on the time-approximation trade-off for the distributed minimum spanning tree problem. SIAM Journal on Computing, 36(2):433--456, 2006.

Digital Library

[5]

[Gaf85] Eli Gafni. Improvements in the time complexity of two message-optimal election algorithms. In Proceedings of the fourth annual ACM symposium on Principles of distributed computing, pages 175--185. ACM, 1985.

Digital Library

[6]

[GHS83] Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Transactions on Programming Languages and systems (TOPLAS), 5(1):66--77, 1983.

[7]

[GKP98] Juan A Garay, Shay Kutten, and David Peleg. A sublinear time distributed algorithm for minimum-weight spanning trees. SIAM Journal on Computing, 27(1):302--316, 1998.

Digital Library

[8]

[GP16] Mohsen Ghaffari and Merav Parter. Mst in log-star rounds of congested clique. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC '16, pages 19--28, New York, NY, USA, 2016. ACM.

Digital Library

[9]

[HPP+15] James W Hegeman, Gopal Pandurangan, Sriram V Pemmaraju, Vivek B Sardeshmukh, and Michele Scquizzato. Toward optimal bounds in the congested clique: Graph connectivity and mst. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, pages 91--100. ACM, 2015.

Digital Library

[10]

[KKT15] Valerie King, Shay Kutten, and Mikkel Thorup. 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, pages 71--80. ACM, 2015.

Digital Library

[11]

[KP95] Shay Kutten and David Peleg. Fast distributed construction of k-dominating sets and applications. In Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing, pages 238--251. ACM, 1995.

Digital Library

[12]

[KPP+15] Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. On the complexity of universal leader election. Journal of the ACM (JACM), 62(1):7, 2015.

Digital Library

[13]

[LPSPP05] Zvi Lotker, Boaz Patt-Shamir, Elan Pavlov, and David Peleg. Minimum-weight spanning tree construction in o (log log n) communication rounds. SIAM Journal on Computing, 35(1):120--131, 2005.

Digital Library

[14]

[Pel00] David Peleg. Distributed computing. SIAM Monographs on discrete mathematics and applications, 5, 2000.

[15]

[PRS16] Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. A time-and message-optimal distributed algorithm for minimum spanning trees. arXiv preprint arXiv:1607.06883, 2016.

[16]

[SHK+12] Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM Journal on Computing, 41(5):1235--1265, 2012.

Cited By

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
https://dl.acm.org/doi/10.5555/3458064.3458190
Mashreghi AKing V(2021)Broadcast and minimum spanning tree with o(m) messages in the asynchronous CONGEST modelDistributed Computing10.1007/s00446-020-00387-yOnline publication date: 8-Feb-2021
https://doi.org/10.1007/s00446-020-00387-y
Elkin M(2020)A Simple Deterministic Distributed MST Algorithm with Near-Optimal Time and Message ComplexitiesJournal of the ACM10.1145/338054667:2(1-15)Online publication date: 5-Apr-2020
https://dl.acm.org/doi/10.1145/3380546
Show More Cited By

Time-communication trade-offs for minimum spanning tree construction
1. Theory of computation

Recommendations

Construction and Impromptu Repair of an MST in a Distributed Network with o(m) Communication
PODC '15: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

In the CONGEST model, a communications network is an undirected graph whose n nodes are processors and whose m edges are the communications links between processors. At any given time step, a message of size O(log n) may be sent by each node to each of ...
Toward Optimal Bounds in the Congested Clique: Graph Connectivity and MST
PODC '15: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

We study two fundamental graph problems, Graph Connectivity (GC) and Minimum Spanning Tree (MST), in the well-studied Congested Clique model, and present several new bounds on the time and message complexities of randomized algorithms for these ...
The expected complexity of Prim's minimum spanning tree algorithm

We study the expected performance of Prim's minimum spanning tree (MST) algorithm implemented using ordinary heaps. We show that this implementation runs in linear or almost linear expected time on a wide range of graphs. This helps to explain why Prim'...

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences

ICDCN '17: Proceedings of the 18th International Conference on Distributed Computing and Networking

January 2017

367 pages

ISBN:9781450348393

DOI:10.1145/3007748

Copyright © 2017 Owner/Author.

This work is licensed under a Creative Commons Attribution-NonCommercial International 4.0 License.

In-Cooperation

IDRBT: IDRBT

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 January 2017

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed limited

Funding Sources

Natural Sciences and Engineering Research Council of Canada

Conference

ICDCN '17

ICDCN '17: 18th International Conference on Distributed Computing and Networking

January 5 - 7, 2017

Hyderabad, India

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
388
Total Downloads

Downloads (Last 12 months)48
Downloads (Last 6 weeks)11

Reflects downloads up to 15 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

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
https://dl.acm.org/doi/10.5555/3458064.3458190
Mashreghi AKing V(2021)Broadcast and minimum spanning tree with o(m) messages in the asynchronous CONGEST modelDistributed Computing10.1007/s00446-020-00387-yOnline publication date: 8-Feb-2021
https://doi.org/10.1007/s00446-020-00387-y
Elkin M(2020)A Simple Deterministic Distributed MST Algorithm with Near-Optimal Time and Message ComplexitiesJournal of the ACM10.1145/338054667:2(1-15)Online publication date: 5-Apr-2020
https://dl.acm.org/doi/10.1145/3380546
Pandurangan GRobinson PScquizzato M(2019)A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning TreesACM Transactions on Algorithms10.1145/336500516:1(1-27)Online publication date: 15-Nov-2019
https://dl.acm.org/doi/10.1145/3365005
Haeupler BHershkowitz DWajc DNewport CKeidar I(2018)Round- and Message-Optimal Distributed Graph AlgorithmsProceedings of the 2018 ACM Symposium on Principles of Distributed Computing10.1145/3212734.3212737(119-128)Online publication date: 23-Jul-2018
https://dl.acm.org/doi/10.1145/3212734.3212737
Elkin MSchiller ESchwarzmann A(2017)A Simple Deterministic Distributed MST Algorithm, with Near-Optimal Time and Message ComplexitiesProceedings of the ACM Symposium on Principles of Distributed Computing10.1145/3087801.3087823(157-163)Online publication date: 25-Jul-2017
https://dl.acm.org/doi/10.1145/3087801.3087823

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Table of Contents