Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

Paola Flocchini, David Ilcinkas, Andrzej Pelc, Nicola Santoro
2012 Algorithmica  
We consider the problem of exploring an anonymous unoriented ring by a team of k identical, oblivious, asynchronous mobile robots that can view the environment but cannot communicate. This weak scenario is standard when the spatial universe in which the robots operate is the two-dimentional plane, but (with one exception) has not been investigated before. We indeed show that, although the lack of these capabilities renders the problems considerably more difficult, ring exploration is still
more » ... ble. We show that the minimum number ρ(n) of robots that can explore a ring of size n is O(log n) and that ρ(n) = Ω(log n) for arbitrarily large n. On one hand we give an algorithm that explores the ring starting from any initial configuration, provided that n and k are co-prime, and we show that there always exist such k in O(log n). On the other hand we show that Ω(log n) agents are necessary for arbitrarily large n. Notice that, when k and n are not co-prime, the problem is sometimes unsolvable (i.e., there are initial configurations for which the exploration cannot be done). This is the case, e.g., when k divides n. Recently a lot of attention has been devoted to the computational and complexity issues arising in systems of autonomous mobile entities located in a spatial universe U. The entities have storage and processing capabilities, exhibit the same behavior (i.e., execute the same protocol), can move in U (their movement is constrained by the nature of U), and are asynchronous in their actions. Depending on the context, the entities are sometimes called agents, other times robots; in the following, we use the latter. The research concern is on determining what tasks can be performed by such entities, under what conditions, and
doi:10.1007/s00453-011-9611-5 fatcat:k3zj2vsdtjedzddojdyry4g6xa