# 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.
Keywords :
Document type :
Reports

Cited literature [13 references]

https://hal.inria.fr/inria-00422100
Contributor : Maria Potop-Butucaru <>
Submitted on : Monday, October 5, 2009 - 5:10:05 PM
Last modification on : Thursday, March 21, 2019 - 12:59:14 PM
Long-term archiving on: Tuesday, June 15, 2010 - 10:27:44 PM

### Files

ReportExploration.pdf
Files produced by the author(s)

### Identifiers

• 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⟩

Record views