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Brief Announcement: Distributed MST Computation in the Sleeping Model: Awake-Optimal Algorithms and Lower Bounds

Authors:

John Augustine,

William K. Moses, Jr.,

Gopal PanduranganAuthors Info & Claims

PODC'22: Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

Pages 51 - 53

https://doi.org/10.1145/3519270.3538459

Published: 21 July 2022 Publication History

Abstract

We study the distributed minimum spanning tree (MST) problem, a fundamental problem in distributed computing. It is well-known that distributed MST can be solved in Õ(D+√n) rounds in the standard CONGEST model (where n is the network size and D is the network diameter) and this is essentially the best possible round complexity (up to logarithmic factors). However, in resource-constrained networks such as wireless ad hoc and sensor networks, nodes spending so much time can lead to significant spending of resources such as energy.

Motivated by the above consideration, we study distributed algorithms for MST under the sleeping model [Chatterjee et al., PODC 2020], a model for design and analysis of resource-efficient distributed algorithms. In the sleeping model, a node can be in one of two modes in any round --- sleeping or awake (unlike the traditional model where nodes are always awake). Only the rounds in which a node is awake are counted, while sleeping rounds are ignored. A node spends resources only in the awake rounds and hence the main goal is to minimize the awake complexity of a distributed algorithm, the worst-case number of rounds any node is awake.

We present distributed MST algorithms that have optimal awake complexity with a matching lower bound. We also show that our awake-optimal algorithms have essentially the best possible round complexity by presenting a lower bound on the product of the awake and round complexity of any distributed algorithm (including randomized).

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References

[1]

Christoph Ambühl. 2005. An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks. In Automata, Languages and Programming, 32nd International Colloquium, ICALP 2005, Lisbon, Portugal, July 11--15, 2005, Proceedings (Lecture Notes in Computer Science, Vol. 3580). Springer, 1139--1150.

[2]

John Augustine, William K. Moses Jr., and Gopal Pandurangan. 2022. Distributed MST Computation in the Sleeping Model: Awake-Optimal Algorithms and Lower Bounds. arXiv preprint arXiv:2204.08385 (2022).

[3]

Leonid Barenboim and Tzalik Maimon. 2021. Deterministic Logarithmic Completeness in the Distributed Sleeping Model. In 35th International Symposium on Distributed Computing, DISC 2021, October 4--8, 2021, Freiburg, Germany (Virtual Conference) (LIPIcs, Vol. 209), Seth Gilbert (Ed.). Schloss Dagstuhl - Leibniz- Zentrum für Informatik, 10:1--10:19. https://doi.org/10.4230/LIPIcs.DISC.2021.10

[4]

Yi-Jun Chang, Varsha Dani, Thomas P. Hayes, Qizheng He, Wenzheng Li, and Seth Pettie. 2018. The energy complexity of broadcast. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing. 95--104.

Digital Library

[5]

Soumyottam Chatterjee, Robert Gmyr, and Gopal Pandurangan. 2020. Sleeping is Efficient: MIS in O(1)-rounds Node-averaged Awake Complexity. In PODC '20: ACM Symposium on Principles of Distributed Computing, Yuval Emek and Christian Cachin (Eds.). 99--108.

Digital Library

[6]

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

[7]

Michael Elkin. 2004. Unconditional lower bounds on the time-approximation tradeoffs for the distributed minimum spanning tree problem. In Proc. of the ACM Symposium on Theory of Computing (Chicago, IL). 331 -- 340.

Digital Library

[8]

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

[9]

R. Gallager, P. Humblet, and P. Spira. 1983. A Distributed Algorithm for Minimum-Weight Spanning Trees. ACM Transactions on Programming Languages and Systems 5, 1 (January 1983), 66--77.

Digital Library

[10]

Mohsen Ghaffari and Bernhard Haeupler. 2016. Distributed Algorithms for Planar Networks II: Low-Congestion Shortcuts, MST, and Min-Cut. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA. SIAM, 202--219.

[11]

Bernhard Haeupler, David Wajc, and Goran Zuzic. 2021. Universally-optimal distributed algorithms for known topologies. In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing. ACM, 1166--1179.

Digital Library

[12]

Maleq Khan, Gopal Pandurangan, and V. S. Anil Kumar. 2009. Distributed Algorithms for Constructing Approximate Minimum Spanning Trees in Wireless Sensor Networks. IEEE Trans. Parallel Distributed Syst. 20, 1 (2009), 124--139.

Digital Library

[13]

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

[14]

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

Digital Library

[15]

Gopal Pandurangan. 2021. Distributed Network Algorithms. In Distributed Network Algorithms. https://sites.google.com/site/gopalpandurangan/home/distributed-network-algorithms

[16]

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

[17]

Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. 2018. The Distributed Minimum Spanning Tree Problem. Bull. EATCS 125 (2018).

[18]

David Peleg. 2000. Distributed Computing: A Locality Sensitive Approach. SIAM.

[19]

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.

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Cited By

Ghaffari MTrygub AKuznetsov PGelles ROlivetti D(2024)A Near-Optimal Low-Energy Deterministic Distributed SSSP with Ramifications on Congestion and APSPProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662812(401-411)Online publication date: 17-Jun-2024
https://doi.org/10.1145/3662158.3662812
Chang YDuan RJiang S(2023)Near-Optimal Time–Energy Tradeoffs for Deterministic Leader ElectionACM Transactions on Algorithms10.1145/361442919:4(1-23)Online publication date: 26-Sep-2023
https://dl.acm.org/doi/10.1145/3614429

Index Terms

Brief Announcement: Distributed MST Computation in the Sleeping Model: Awake-Optimal Algorithms and Lower Bounds
1. Mathematics of computing
  1. Discrete mathematics
  2. Probability and statistics
    1. Probabilistic algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms

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Published In

cover image ACM Conferences

PODC'22: Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

July 2022

509 pages

ISBN:9781450392624

DOI:10.1145/3519270

General Chair:
Alessia Milani
Aix-Marseille University, France
,
Program Chair:
Philipp Woelfel
University of Calgary, Canada

Copyright © 2022 Owner/Author.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Publication History

Published: 21 July 2022

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DST/SERB MATRICS
Centre of Excellence in Cryptography Cybersecurity and Distributed Trust under the IIT Madras Institute of Eminence Scheme
VAJRA visiting faculty program of the Government of India
NSF (National Science Foundation)
U.S.-Israel Binational Science Foundation (BSF)

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PODC '22

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PODC '22: ACM Symposium on Principles of Distributed Computing

July 25 - 29, 2022

Salerno, Italy

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Cited By

Ghaffari MTrygub AKuznetsov PGelles ROlivetti D(2024)A Near-Optimal Low-Energy Deterministic Distributed SSSP with Ramifications on Congestion and APSPProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662812(401-411)Online publication date: 17-Jun-2024
https://doi.org/10.1145/3662158.3662812
Chang YDuan RJiang S(2023)Near-Optimal Time–Energy Tradeoffs for Deterministic Leader ElectionACM Transactions on Algorithms10.1145/361442919:4(1-23)Online publication date: 26-Sep-2023
https://dl.acm.org/doi/10.1145/3614429

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