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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Bibliographic Details
Published in:Journal of applied probability Vol. 58; no. 2; pp. 394 - 410
Main Authors: Mocquard, Yves, Robin, Frédérique, Séricola, Bruno, Anceaume, Emmanuelle
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.06.2021
Applied Probability Trust
Cambridge University press
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2020.97