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Simple Majority Consensus in Networks with Unreliable Communication †

In this work, we analyze the performance of a simple majority-rule protocol solving a fundamental coordination problem in distributed systems—binary majority consensus—in the presence of probabilistic message loss. Using probabilistic analysis for a large-scale, fully-connected, network of [Formula:...

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Detalles Bibliográficos
Autores principales: Tamir, Ran, Livshits, Ariel, Shadmi, Yonatan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947436/
https://www.ncbi.nlm.nih.gov/pubmed/35327844
http://dx.doi.org/10.3390/e24030333
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author Tamir, Ran
Livshits, Ariel
Shadmi, Yonatan
author_facet Tamir, Ran
Livshits, Ariel
Shadmi, Yonatan
author_sort Tamir, Ran
collection PubMed
description In this work, we analyze the performance of a simple majority-rule protocol solving a fundamental coordination problem in distributed systems—binary majority consensus—in the presence of probabilistic message loss. Using probabilistic analysis for a large-scale, fully-connected, network of [Formula: see text] agents, we prove that the Simple Majority Protocol (SMP) reaches consensus in only three communication rounds, with probability approaching 1 as n grows to infinity. Moreover, if the difference between the numbers of agents that hold different opinions grows at a rate of [Formula: see text] , then the SMP with only two communication rounds attains consensus on the majority opinion of the network, and if this difference grows faster than [Formula: see text] , then the SMP reaches consensus on the majority opinion of the network in a single round, with probability converging to 1 as exponentially fast as [Formula: see text]. We also provide some converse results, showing that these requirements are not only sufficient, but also necessary.
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spelling pubmed-89474362022-03-25 Simple Majority Consensus in Networks with Unreliable Communication † Tamir, Ran Livshits, Ariel Shadmi, Yonatan Entropy (Basel) Article In this work, we analyze the performance of a simple majority-rule protocol solving a fundamental coordination problem in distributed systems—binary majority consensus—in the presence of probabilistic message loss. Using probabilistic analysis for a large-scale, fully-connected, network of [Formula: see text] agents, we prove that the Simple Majority Protocol (SMP) reaches consensus in only three communication rounds, with probability approaching 1 as n grows to infinity. Moreover, if the difference between the numbers of agents that hold different opinions grows at a rate of [Formula: see text] , then the SMP with only two communication rounds attains consensus on the majority opinion of the network, and if this difference grows faster than [Formula: see text] , then the SMP reaches consensus on the majority opinion of the network in a single round, with probability converging to 1 as exponentially fast as [Formula: see text]. We also provide some converse results, showing that these requirements are not only sufficient, but also necessary. MDPI 2022-02-25 /pmc/articles/PMC8947436/ /pubmed/35327844 http://dx.doi.org/10.3390/e24030333 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Tamir, Ran
Livshits, Ariel
Shadmi, Yonatan
Simple Majority Consensus in Networks with Unreliable Communication †
title Simple Majority Consensus in Networks with Unreliable Communication †
title_full Simple Majority Consensus in Networks with Unreliable Communication †
title_fullStr Simple Majority Consensus in Networks with Unreliable Communication †
title_full_unstemmed Simple Majority Consensus in Networks with Unreliable Communication †
title_short Simple Majority Consensus in Networks with Unreliable Communication †
title_sort simple majority consensus in networks with unreliable communication †
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947436/
https://www.ncbi.nlm.nih.gov/pubmed/35327844
http://dx.doi.org/10.3390/e24030333
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