Ring Exploration with Myopic Luminous Robots
Fukuhito Ooshita, S\'ebastien Tixeuil

TL;DR
This paper studies how limited visibility and minimal light colors affect the ability of autonomous robots to explore ring networks, establishing the minimal number of robots needed under various synchrony models.
Contribution
It provides the first tight bounds on the number of myopic luminous robots required for exploration in ring networks across different synchrony models.
Findings
Two and three robots suffice for perpetual and terminating exploration in fully synchronous models.
Three and four robots are necessary and sufficient in semi-synchronous and asynchronous models.
Lights with two colors significantly reduce the number of robots needed compared to no lights.
Abstract
We investigate exploration algorithms for autonomous mobile robots evolving in uniform ring-shaped networks. Different from the usual Look-Compute-Move (LCM) model, we consider two characteristics: myopia and luminosity. Myopia means each robot has a limited visibility. We consider the weakest assumption for myopia: each robot can only observe its neighboring nodes. Luminosity means each robot maintains a non-volatile visible light. We consider the weakest assumption for luminosity: each robot can use only two colors for its light. The main interest of this paper is to clarify the impact of luminosity on exploration with myopic robots. As a main contribution, we prove that 1) in the fully synchronous model, two and three robots are necessary and sufficient to achieve perpetual and terminating exploration, respectively, and 2) in the semi-synchronous and asynchronous models, three and…
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