Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots

Stéphane Devismes Franck Petit Sébastien Tixeuil 1
1 NPA - Networks and Performance Analysis
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We consider a team of k identical, oblivious, asynchronous mobile robots that are able to sense (i.e., view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by deterministic robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the exploration problem of anonymous unoriented rings of any size. It is known that Theta(log n) robots are necessary and sufficient to solve the problem with k deterministic robots, provided that k and n are coprime. By contrast, we show that four identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01295189
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Submitted on : Wednesday, March 30, 2016 - 3:07:54 PM
Last modification on : Thursday, March 21, 2019 - 1:06:43 PM

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Stéphane Devismes, Franck Petit, Sébastien Tixeuil. Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots. Sirocco 2009, May 2009, Piran, Slovenia. pp.195-208, ⟨10.1007/978-3-642-11476-2_16⟩. ⟨hal-01295189⟩

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