Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots

Stéphane Devismes (1) , Franck Petit (2, 3) , Sébastien Tixeuil (4, 5)

1 VERIMAG - IMAG - VERIMAG
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 GRAAL - Algorithms and Scheduling for Distributed Heterogeneous Platforms
4 GRAND-LARGE - Global parallel and distributed computing
5 NPA - Networks and Performance Analysis

We consider a team of $k$ identical, oblivious, asynchronous mobile robots that are able to sense (\emph{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 \emph{deterministic} robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the \emph{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 \emph{four} identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.

Keywords: Robots; Anonimity; Obliviousness; Exploration

Domains: Data Structures and Algorithms [cs.DS]; Distributed, Parallel, and Cluster Computing [cs.DC]; Mobile Computing; Computational Complexity [cs.CC]; Robotics [cs.RO]

Stéphane Devismes, Franck Petit, Sébastien Tixeuil. Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots. [Research Report] RR-6838, INRIA. 2009, pp.29. ⟨inria-00360305⟩