Stochastic analysis of average-based distributed algorithms

We analyze average-based distributed algorithms relying on simple and pairwise random interactions among a large and unknown number of anonymous agents. This allows the characterization of global properties emerging from these local interactions. Agents start with an initial integer value, and at ea...

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Vydáno v:Journal of applied probability Ročník 58; číslo 2; s. 394 - 410
Hlavní autoři: Mocquard, Yves, Robin, Frédérique, Séricola, Bruno, Anceaume, Emmanuelle
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.06.2021
Applied Probability Trust
Cambridge University press
Témata:
Algorithms
Computer Science
Convergence
Data Structures and Algorithms
Distributed, Parallel, and Cluster Computing
Integers
Internet of Things
Original Article
Population
Research Papers
Stochastic models
Markov chain
60J10
coupling
Averaging stochastic process
distributed algorithms
interacting particle systems
60K35
Coupling
Distributed algorithms
Interacting particle systems
ISSN:0021-9002, 1475-6072
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Abstract We analyze average-based distributed algorithms relying on simple and pairwise random interactions among a large and unknown number of anonymous agents. This allows the characterization of global properties emerging from these local interactions. Agents start with an initial integer value, and at each interaction keep the average integer part of both values as their new value. The convergence occurs when, with high probability, all the agents possess the same value, which means that they all know a property of the global system. Using a well-chosen stochastic coupling, we improve upon existing results by providing explicit and tight bounds on the convergence time. We apply these general results to both the proportion problem and the system size problem.
AbstractList We analyze average-based distributed algorithms relying on simple and pairwise random interactions among a large and unknown number of anonymous agents. This allows the characterization of global properties emerging from these local interactions. Agents start with an initial integer value, and at each interaction keep the average integer part of both values as their new value. The convergence occurs when, with high probability, all the agents possess the same value, which means that they all know a property of the global system. Using a well-chosen stochastic coupling, we improve upon existing results by providing explicit and tight bounds on the convergence time. We apply these general results to both the proportion problem and the system size problem.
We analyse average-based distributed algorithms relying on simple and pairwise random interactions among a large and unknown number of anonymous agents. This allows the characterization of global properties emerging from these local interactions. Agents start with an initial integer value, and at each interaction keep the average integer part of both values as their new value. The convergence occurs when, with high probability, all the agents possess the same value which means that they all know a property of the global system. Using a well chosen stochastic coupling, we improve upon existing results by providing explicit and tight bounds of the convergence time. We apply these general results to both the proportion problem and the system size problem.
Author Séricola, Bruno
Anceaume, Emmanuelle
Mocquard, Yves
Robin, Frédérique
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  surname: Séricola
  fullname: Séricola, Bruno
  email: bruno.sericola@inria.fr
  organization: Inria, Univ. Rennes, CNRS, IRISA
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  givenname: Emmanuelle
  surname: Anceaume
  fullname: Anceaume, Emmanuelle
  organization: CNRS, Univ. Rennes, Inria, IRISA
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Cites_doi 10.1287/ijoc.2018.0845
10.1214/11-PS184
10.1214/EJP.v20-3559
10.1007/978-1-4613-8542-4
10.1016/j.jtbi.2013.06.024
10.1109/NCA.2015.35
10.1017/jpr.2016.94
10.1007/s00446-005-0138-3
10.1214/EJP.v20-3582
ContentType Journal Article
Copyright The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust
The Author(s), 2021
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Keywords Markov chain
60J10
coupling
Averaging stochastic process
distributed algorithms
interacting particle systems
60K35
Coupling
Distributed algorithms
Interacting particle systems
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SubjectTerms Algorithms
Computer Science
Convergence
Data Structures and Algorithms
Distributed, Parallel, and Cluster Computing
Integers
Internet of Things
Original Article
Population
Research Papers
Stochastic models
Title Stochastic analysis of average-based distributed algorithms
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