Gathering on Rings for Myopic Asynchronous Robots with Lights

• Published in: Theory of computing systems Vol. 69; no. 1; p. 8
• Main Authors: Kamei, Sayaka, Lamani, Anissa, Ooshita, Fukuhito, Tixeuil, Sébastien, Wada, Koichi
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2025; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Computer Science; Configurations; Nodes; Robots; Theory of Computation; Visibility; Luminous; Gathering; LCM robot systems; Myopic
• ISSN: 1432-4350; 1433-0490
• DOI: 10.1007/s00224-024-10199-3

We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: M init , which denotes the number of nodes between two border nodes, and N init , which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that may see other robots on exactly one side. Our main contribution is to prove that, if M init or N init is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility.