Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots [article]

Stéphane Devismes, Franck Petit (LIP, INRIA Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme), Sébastien Tixeuil
2009 arXiv   pre-print
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
more » ... any size. It is known that Θ( 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.
arXiv:0902.1834v1 fatcat:32xmhg35avgebe26iorsnioazq