research-article

Towards Optimal Synchronous Counting

Authors:

Christoph Lenzen,

Joel Rybicki,

Jukka SuomelaAuthors Info & Claims

PODC '15: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

Pages 441 - 450

https://doi.org/10.1145/2767386.2767423

Published: 21 July 2015 Publication History

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Abstract

Consider a complete communication network of n nodes, in which the nodes receive a common clock pulse. We study the synchronous c-counting problem: given any starting state and up to f faulty nodes with arbitrary behaviour, the task is to eventually have all correct nodes count modulo c in agreement. Thus, we are considering algorithms that are self-stabilising despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have linear stabilisation time in f, (3) use a small number of states, and (4) achieve almost-optimal resilience. Prior algorithms either resort to randomisation, use a large number of states, or have poor resilience. In particular, we achieve an exponential improvement in the state complexity of deterministic algorithms, while still achieving linear stabilisation time and almost-linear resilience.

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Cited By

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Yu SZhu JYang J(2021)Reaching self-stabilising distributed synchronisation with COTS Ethernet components: the WALDEN approachReal-Time Systems10.1007/s11241-020-09356-x57:4(347-386)Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s11241-020-09356-x
Boczkowski LKorman ANatale E(2019)Minimizing message size in stochastic communication patternsDistributed Computing10.1007/s00446-018-0330-x32:3(173-191)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s00446-018-0330-x
Boczkowski LKorman ANatale EKlein P(2017)Minimizing message size in stochastic communication patternsProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039854(2540-2559)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039854
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Towards Optimal Synchronous Counting

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Published In

PODC '15: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

July 2015

508 pages

ISBN:9781450336178

DOI:10.1145/2767386

General Chair:
Chryssis Georgiou
University of Cyprus, Cyprus
,
Program Chair:
Paul G. Spirakis
University of Liverpool, UK & CTI, Greece

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 July 2015

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PODC '15

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PODC '15: ACM Symposium on Principles of Distributed Computing

July 21 - 23, 2015

Donostia-San Sebastián, Spain

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PODC '15 Paper Acceptance Rate 45 of 191 submissions, 24%;

Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

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Yu SZhu JYang J(2021)Reaching self-stabilising distributed synchronisation with COTS Ethernet components: the WALDEN approachReal-Time Systems10.1007/s11241-020-09356-x57:4(347-386)Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s11241-020-09356-x
Boczkowski LKorman ANatale E(2019)Minimizing message size in stochastic communication patternsDistributed Computing10.1007/s00446-018-0330-x32:3(173-191)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s00446-018-0330-x
Boczkowski LKorman ANatale EKlein P(2017)Minimizing message size in stochastic communication patternsProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039854(2540-2559)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039854
Dolev DHeljanko KJärvisalo MKorhonen JLenzen CRybicki JSuomela JWieringa S(2016)Synchronous counting and computational algorithm designJournal of Computer and System Sciences10.1016/j.jcss.2015.09.00282:2(310-332)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1016/j.jcss.2015.09.002
Lenzen CRybicki J(2016)Near-Optimal Self-stabilising Counting and Firing SquadsStabilization, Safety, and Security of Distributed Systems10.1007/978-3-319-49259-9_21(263-280)Online publication date: 3-Nov-2016
https://doi.org/10.1007/978-3-319-49259-9_21
Lenzen CRybicki J(2015)Efficient Counting with Optimal ResilienceProceedings of the 29th International Symposium on Distributed Computing - Volume 936310.1007/978-3-662-48653-5_2(16-30)Online publication date: 7-Oct-2015
https://dl.acm.org/doi/10.1007/978-3-662-48653-5_2

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