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Brief Announcement: A Time and Space Optimal Stable Population Protocol Solving Exact Majority

Authors:

Mahsa Eftekhari,

Leszek Gąsieniec,

Grzegorz Stachowiak,

Przemyslaw UznańskiAuthors Info & Claims

PODC'21: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

Pages 77 - 80

https://doi.org/10.1145/3465084.3467942

Published: 23 July 2021 Publication History

Abstract

We study population protocols, a model of distributed computing where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied majority problem is that of determining in an initial population of n agents, each with one of two opinions A or B, whether there are more A, more B, or a tie. A stable protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of A, B, or T, from which the consensus cannot change. We describe a protocol that solves this problem using O(log n) states (log log n + O(1) bits of memory) and optimal expected time O(log n). The number of states O(log n) is known to be optimal for the class of polylogarithmic time stable protocols that are "output dominant'' and "monotone''. These are two natural constraints satisfied by our protocol, making it simultaneously time- and state-optimal for that class. Our protocol is nonuniform : the transition function has the value log n encoded in it. We show that the protocol can be modified to be uniform, while increasing the state complexity to Θ(log n log log n).

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References

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https://github.com/UC-Davis-molecular-computing/ppsim/blob/main/examples/majority.ipynb.

[2]

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Andreas Bilke, Colin Cooper, Robert Elsässer, and Tomasz Radzik. Brief announcement: Population protocols for leader election and exact majority with O(log 2 n) states and O(log 2 n) convergence time. In PODC 2017: Proceedings of the ACM Symposium on Principles of Distributed Computing, pages 451--453. ACM, 2017.

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David Doty and Mahsa Eftekhari. Efficient size estimation and impossibility of termination in uniform dense population protocols. In PODC 2019: Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, pages 34--42, 2019.

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Leszek Gasieniec and Grzegorz Stachowiak. Fast space optimal leader election in population protocols. In SODA 2018: ACM-SIAM Symposium on Discrete Algorithms, pages 2653--2667. SIAM, 2018.

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George B Mertzios, Sotiris E Nikoletseas, Christoforos L Raptopoulos, and Paul G Spirakis. Determining majority in networks with local interactions and very small local memory. In International Colloquium on Automata, Languages, and Programming, pages 871--882. Springer, 2014.

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Cited By

Gańczorz AGąsieniec LJurdziński TKowalski JStachowiak G(2024)Selective Population ProtocolsStabilization, Safety, and Security of Distributed Systems10.1007/978-3-031-74498-3_16(225-239)Online publication date: 20-Oct-2024
https://doi.org/10.1007/978-3-031-74498-3_16
Doty DEftekhari M(2021)A survey of size counting in population protocolsTheoretical Computer Science10.1016/j.tcs.2021.08.038894(91-102)Online publication date: Nov-2021
https://doi.org/10.1016/j.tcs.2021.08.038

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Brief Announcement: A Time and Space Optimal Stable Population Protocol Solving Exact Majority

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Published In

cover image ACM Conferences

PODC'21: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

July 2021

590 pages

ISBN:9781450385480

DOI:10.1145/3465084

General Chair:
Avery Miller
University of Manitoba, Canada
,
Program Chair:
Keren Censor-Hillel
Technion, Israel

Copyright © 2021 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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Published: 23 July 2021

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PODC '21: ACM Symposium on Principles of Distributed Computing

July 26 - 30, 2021

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

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Cited By

Gańczorz AGąsieniec LJurdziński TKowalski JStachowiak G(2024)Selective Population ProtocolsStabilization, Safety, and Security of Distributed Systems10.1007/978-3-031-74498-3_16(225-239)Online publication date: 20-Oct-2024
https://doi.org/10.1007/978-3-031-74498-3_16
Doty DEftekhari M(2021)A survey of size counting in population protocolsTheoretical Computer Science10.1016/j.tcs.2021.08.038894(91-102)Online publication date: Nov-2021
https://doi.org/10.1016/j.tcs.2021.08.038

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