The Mutual Visibility Problem for Fat Robots with Lights
DOI:
https://doi.org/10.57717/cgt.v5i1.81Abstract
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 pointrobots [Di Luna et al., Information and Computation, 2017].
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Copyright (c) 2026 Rusul J. Alsaedi, Joachim Gudmundsson, André van Renssen
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