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Stochastic analysis of average-based distributed algorithms

Part of: Special processes Markov processes

Published online by Cambridge University Press:  23 June 2021

Yves Mocquard ,
Frédérique Robin ,
Bruno Séricola  and
Emmanuelle Anceaume
Yves Mocquard*
Affiliation:
Inria, Univ. Rennes, CNRS, IRISA
Frédérique Robin*
Affiliation:
Inria, Univ. Rennes, CNRS, IRISA
Bruno Séricola*
Affiliation:
Inria, Univ. Rennes, CNRS, IRISA
Emmanuelle Anceaume*
Affiliation:
CNRS, Univ. Rennes, Inria, IRISA
*
*Postal address: Inria, Campus de Beaulieu, 35042 Rennes Cedex, France.
*Postal address: Inria, Campus de Beaulieu, 35042 Rennes Cedex, France.
*Postal address: Inria, Campus de Beaulieu, 35042 Rennes Cedex, France.
***Postal address: IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France.
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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.

Keywords

Averaging stochastic processinteracting particle systemsMarkov chaincouplingdistributed algorithms

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 2 , June 2021 , pp. 394 - 410
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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