Dynamic size counting in the population protocol model

The population protocol model describes collections of distributed agents that interact in pairs to solve a common task. We consider a dynamic variant of this prominent model, where we assume that an adversary may change the population size at an arbitrary point in time. In this model we tackle the problem of counting the population size: in the dynamic size counting problem the goal is to design an algorithm that computes an approximation of log n. This estimate can be used to turn static, non-uniform population protocols, i.e., protocols that depend on the population size n, into dynamic and loosely-stabilizing protocols.Our contributions in this paper are three-fold. Starting from an arbitrary initial configuration, we first prove that the agents converge quickly to a valid configuration where each agent has a constant-factor approximation of log n, and once the agents reach such a valid configuration, they stay in it for a polynomial number of time steps. Second, we show how to use our protocol to define a uniform and loosely-stabilizing phase clock for the population protocol model. Finally, we support our theoretical findings by empirical simulations that show that our protocols work well in practice.

Subjects

loose stabilization

phase clocks

population protocols

size counting

DDC Class

510: Mathematics

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publishedVersion

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https://creativecommons.org/licenses/by/4.0/

Name

3662158.3662825.pdf

Type

Main Article

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687.27 KB

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Adobe PDF

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Dynamic size counting in the population protocol model