Stand-Up Indulgent Gathering on Lines for Myopic Luminous Robots
CoRR(2023)
Abstract
We consider a strong variant of the crash fault-tolerant gathering problem
called stand-up indulgent gathering (SUIG), by robots endowed with limited
visibility sensors and lights on line-shaped networks. In this problem, a group
of mobile robots must eventually gather at a single location, not known
beforehand, regardless of the occurrence of crashes. Differently from previous
work that considered unlimited visibility, we assume that robots can observe
nodes only within a certain fixed distance (that is, they are myopic), and emit
a visible color from a fixed set (that is, they are luminous), without
multiplicity detection. We consider algorithms depending on two parameters
related to the initial configuration: $M_{init}$, which denotes the number of
nodes between two border nodes, and $O_{init}$, 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 cannot see other robots on at least one
side. Our main contribution is to prove that, if $M_{init}$ or $O_{init}$ is
odd, SUIG can be solved in the fully synchronous model.
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