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arXiv · 0902.1834

Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots

Stéphane Devismes·Franck Petit·Sébastien Tixeuil
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Abstract

We consider a team of $k$ identical, oblivious, asynchronous mobile robots that are able to sense (\emph{i.e.}, view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by \emph{deterministic} robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the \emph{exploration} problem of anonymous unoriented rings of any size. It is known that $Θ(\log n)$ robots are necessary and sufficient to solve the problem with $k$ deterministic robots, provided that $k$ and $n$ are coprime. By contrast, we show that \emph{four} identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.

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Stéphane Devismes, Franck Petit, Sébastien Tixeuil. 2009-02-11. Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots. https://arxiv.org/abs/0902.1834

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