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Reports (Research Report) Year : 2009

Optimal deterministic ring exploration with oblivious asynchronous robots

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Anissa Lamani
Maria Potop-Butucaru
• Function : Author
• PersonId : 841868
Sébastien Tixeuil

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.

Dates and versions

inria-00422100 , version 1 (05-10-2009)

Identifiers

• HAL Id : inria-00422100 , version 1
• ARXIV :

Cite

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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