# Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

Abstract : We consider the problem of exploring an anonymous unoriented ring by a team of $k$ identical, oblivious, asynchronous mobile robots that can view the environment but cannot communicate. This weak scenario is standard when the spatial universe in which the robots operate is the two-dimentional plane, but (with one exception) has not been investigated before. We indeed show that, although the lack of these capabilities renders the problems considerably more difficult, ring exploration is still possible. We show that the minimum number $\rho(n)$ of robots that can explore a ring of size $n$ is $O(\log n)$ and that $\rho(n)=\Omega(\log n)$ for arbitrarily large $n$. On one hand we give an algorithm that explores the ring starting from any initial configuration, provided that $n$ and $k$ are co-prime, and we show that there always exist such $k$ in $O(\log n)$. On the other hand we show that $\Omega(\log n)$ agents are necessary for arbitrarily large $n$. Notice that, when $k$ and $n$ are not co-prime, the problem is sometimes unsolvable (i.e., there are initial configurations for which the exploration cannot be done). This is the case, e.g., when $k$ divides $n$.
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https://hal.archives-ouvertes.fr/hal-00339884
Contributor : David Ilcinkas <>
Submitted on : Wednesday, November 19, 2008 - 12:08:35 PM
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### Citation

Paola Flocchini, David Ilcinkas, Andrzej Pelc, Nicola Santoro. Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots. OPODIS 2007, Dec 2007, Pointe à Pitre, Guadeloupe, France. pp.105-118, ⟨10.1007/978-3-540-77096-1_8⟩. ⟨hal-00339884⟩

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