Optimal probabilistic ring exploration by semi-synchronous oblivious robots

Authors:
Stéphane Devismes;Franck Petit;Sébastien Tixeuil
Affiliations:
VERIMAG UMR 5104, Université Joseph Fourier, Grenoble, France;LIP6 UMR 7606, UPMC Sorbonne Universités, France;LIP6 UMR 7606, UPMC Sorbonne Universités, France
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

We consider a team of k identical, oblivious, and semi-synchronous 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 n. It is known that k=@Q(logn) deterministic robots are necessary and sufficient to solve the problem, 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.