Given a set of n≥1 unit disk robots in the Euclidean plane, we consider the fundamental problem of providing mutual visibility to them: the robots must reposition themselves to reach a configuration where they all see each other. This problem arises under obstructed visibility, where a robot cannot see another robot if there is a third robot on the straight line segment between them. This problem was solved by Sharma et al. [ICDCN, 2018] in the luminous robots model, where each robot is equipped with an externally visible light that can assume colors from a fixed set of colors, using 9 colors and O(n) rounds. In this work, we present an algorithm that requires only 2 colors and O(n) rounds. The number of colors is optimal since at least two colors are required even for point robots [Di Luna et al., Information and Computation, 2017].
@article{arxiv.2206.14423,
title = {The Mutual Visibility Problem for Fat Robots with Lights},
author = {Rusul J. Alsaedi and Joachim Gudmundsson and André van Renssen},
journal= {arXiv preprint arXiv:2206.14423},
year = {2026}
}