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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:...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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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. |
format | Online Article Text |
id | pubmed-8947436 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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