# Optimal deterministic ring exploration with oblivious asynchronous robots

2 Regal - Large-Scale Distributed Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : We consider the problem of exploring an anonymous unoriented ring of size $n$ by $k$ identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that $k$ must not divide $n$ for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size $n$ is $4$. An upper bound of $17$ robots holds in the deterministic case while $4$ probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots whenever the size of the ring is even, and that five robots are sufficient for any $n$ that is coprime with five. Our protocol completes exploration in $O(n)$ robot moves, which is also optimal.
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Rapport
[Research Report] 2009, pp.23
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https://hal.inria.fr/inria-00422100
Contributeur : Maria Potop-Butucaru <>
Soumis le : lundi 5 octobre 2009 - 17:10:05
Dernière modification le : vendredi 31 août 2018 - 09:25:53
Document(s) archivé(s) le : mardi 15 juin 2010 - 22:27:44

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ReportExploration.pdf
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• HAL Id : inria-00422100, version 1
• ARXIV : 0910.0832

### Citation

Anissa Lamani, Maria Potop-Butucaru, Sébastien Tixeuil. Optimal deterministic ring exploration with oblivious asynchronous robots. [Research Report] 2009, pp.23. 〈inria-00422100〉

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