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# Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots

3 GRAAL - Algorithms and Scheduling for Distributed Heterogeneous Platforms
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
4 GRAND-LARGE - Global parallel and distributed computing
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LIFL - Laboratoire d'Informatique Fondamentale de Lille, LRI - Laboratoire de Recherche en Informatique
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 $\Theta(\log n)$ 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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https://hal.inria.fr/inria-00360305
Contributor : Sébastien Tixeuil Connect in order to contact the contributor
Submitted on : Tuesday, February 10, 2009 - 9:45:13 PM
Last modification on : Friday, February 4, 2022 - 3:31:54 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 7:20:32 PM

### Files

RR-6838.pdf
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### Identifiers

• HAL Id : inria-00360305, version 1
• ARXIV : 0902.1834

### Citation

Stéphane Devismes, Franck Petit, Sébastien Tixeuil. Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots. [Research Report] RR-6838, INRIA. 2009, pp.29. ⟨inria-00360305⟩

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