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Optimal Deterministic Ring Exploration with Oblivious Asynchronous Robots

Anissa Lamani 1 Maria Gradinariu Potop-Butucaru 1 Sébastien Tixeuil 2
1 Regal - Large-Scale Distributed Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
2 NPA - Networks and Performance Analysis
LIP6 - Laboratoire d'Informatique de Paris 6
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, 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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Submitted on : Friday, March 25, 2016 - 3:23:34 PM
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Anissa Lamani, Maria Gradinariu Potop-Butucaru, Sébastien Tixeuil. Optimal Deterministic Ring Exploration with Oblivious Asynchronous Robots. 17th International Colloquium Structural Information and Communication Complexity, SIROCCO, 2010, Şirince, Turkey. pp.183-196, ⟨10.1007/978-3-642-13284-1_15⟩. ⟨hal-01293850⟩



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