Average-based Population Protocols : Explicit and Tight Bounds of the Convergence Time
Abstract
The computational model of population protocols is a formalism that allows the analysis of properties emerging from simple and pairwise interactions among a very large number of anonymous finite-state agents. Among the different problems addressed in this model, average-based problems have been studied for the last few years. In these problems, agents start independently from each other with an initial integer state, and at each interaction with another agent, keep the average of their states as their new state. In this paper, using a well chosen stochastic coupling, we considerably improve upon existing results by providing explicit and tight bounds of the time required to converge to the solution of these problems. We apply these general results to the proportion problem, which consists for each agent to compute the proportion of agents that initially started in one predetermined state, and to the counting population size problem, which aims at estimating the size of the system. Both protocols are uniform, i.e., each agent's local algorithm for computing the outputs, given the inputs, does not require the knowledge of the number of agents. Numerical simulations illustrate our bounds of the convergence time, and show that these bounds are tight in the sense that among extensive simulations, numerous ones exactly fit with our bounds.
Keywords
yvesmocquard@irisafr
26 pages https://doiorg/10 1145/nnnnnnnnnnnnnn Authors' addresses: Yves Mocquard
1 (July 2019)
and Emmanuelle Anceaume 2019 Average-based Population Protocols : Explicit and Tight Bounds of the Convergence Time 1
CCS Concepts: • Mathematics of computing → Probabilistic algorithms Additional Key Words and Phrases: ACM Reference Format: Yves Mocquard
Univ Rennes
CNRS
IRISA
Campus de beaulieu
Rennes
France
Frédérique Robin
frederiquerobin@inriafr
Inria
Université Paris-Saclay -LMS
Ecole Polytechnique
Université Paris-Saclay
1 Rue Honoré d'Estienne d'Orves
Palaiseau
Bruno Sericola
brunosericola@inriafr
Emmanuelle Anceaume
emmanuelleanceaume@irisafr
Origin | Files produced by the author(s) |
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