Article Dans Une Revue Theory of Computing Systems Année : 2025

Gathering on Rings for Myopic Asynchronous Robots with Lights

Résumé

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.
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Dates et versions

hal-04910697 , version 1 (24-01-2025)

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Sayaka Kamei, Anissa Lamani, Fukuhito Ooshita, Sébastien Tixeuil, Koichi Wada. Gathering on Rings for Myopic Asynchronous Robots with Lights. Theory of Computing Systems, 2025, 69 (1), pp.8. ⟨10.1007/s00224-024-10199-3⟩. ⟨hal-04910697⟩
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