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Gathering on Rings for Myopic Asynchronous Robots With Lights Sébastien Tixeuil

Abstract : 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: Minit, which denotes the number of nodes between two border nodes, and Oinit, 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 cannot see other robots on at least one side. Our main contribution is to prove that, if Minit or Oinit 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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https://hal.sorbonne-universite.fr/hal-02475374
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Sayaka Kamei, Anissa Lamani, Fukuhito Ooshita, Sébastien Tixeuil, Koichi Wada. Gathering on Rings for Myopic Asynchronous Robots With Lights Sébastien Tixeuil. 23rd International Conference on Principles of Distributed Systems (OPODIS 2019), Dec 2019, Neuchatel, Netherlands. pp.27:1--27:17, ⟨10.4230/LIPIcs.OPODIS.2019.27⟩. ⟨hal-02475374⟩

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