Ring Exploration by Oblivious Agents with Local Vision

Abstract

International audienceThe problem of exploring a discrete environment by identical oblivious asynchronous agents (or robots) devoid of direct means of communication has been well investigated so far. The (terminating) exploration requires that starting from a configuration where no two agents occupy the same node, every node needs to be visited by at least one agent, with the additional constraint that all agents eventually stop moving. Agents have sensors that allow them to see their environment and move accordingly. The previous works on this problem assume agents having an unlimited visibility, that is, they can sense the agents on every node of the ring, whatever the ring size. In this paper, we address deterministic exploration in an anonymous, unoriented ring using oblivious, and myopic agents. By myopic, we mean that their visibility is limited in terms of sensing distance. We consider the strongest possible myopia that is, an agent can only sense agents located at its own and at its immediate neighboring nodes. Our contribution is threefold. We first prove that within such settings, no deterministic exploration is possible in the semi-synchronous model. The result is also valid for the (fully) asynchronous model and holds for any k < n where k is the number of agents and n is the number of nodes in the ring. Next, we address the synchronous model and show that no deterministic exploration protocol solves the problem with less than five agents when n > 6. Finally, we provide optimal (in terms of number of agents) deterministic algorithms in the fully synchronous model for both cases 2 < n < 7 and n > 6

Oblivious Robots on Graphs: Exploration

“…Limited visibility has also been considered, for deterministic algorithms, and in the case of global (up to the visibility radius) strong multiplicity detection. When the visibility radius ρ is 1, even a limited amount of asynchrony renders the problem impossible to solve: there are no deterministic algorithms working in the Ssync model, for any number k < n of robots [11]. In the same paper, the authors show that 5 robots are necessary in the Fsync model, and they present an algorithm for 5 robots working when all robots are on consecutive vertices in the initial configuration.…”

Deterministic Dispersion of Mobile Robots in Dynamic Rings

“…A robot is myopic when its visibility is restricted to a subset of nodes of the entire ring. [8] provides positive and negative results for varied degrees of myopicness of robots for different levels of synchronicity of networks. Of particular interest, they provide synchronous deterministic algorithms for robots with no visibility to explore a static ring.…”

“…Exploration of rings by mobile robots has been a long studied problem and there is much literature on it. In particular, several works have studied deterministic exploration of anonymous, unoriented rings by oblivious robots that relied on their view of the ring to make decisions [25,8,9,16]. Exploration in an asynchronous setting was studied in [25,16,9] while [8] looked into the synchronous setting.…”

Terminating Grid Exploration with Myopic Luminous Robots

“…However, the capability of the unlimited visibility seems powerful and somewhat contradicts the principle of weak mobile robots. For this reason, some studies consider the more realistic case of myopic robots [8,9]. A myopic robot has limited visibility, i.e., it can see nodes (and robots on them) only within a certain fixed distance φ. Datta et al studied the terminating exploration of rings for φ = 1 [8] and φ = 2, 3 [9].…”