Meeting in a Polygon by Anonymous Oblivious Robots
Giuseppe A. Di Luna, Paola Flocchini, Nicola Santoro, Giovanni, Viglietta, and Masafumi Yamashita

TL;DR
This paper studies the Meeting problem for anonymous, oblivious robots in polygons, establishing tight bounds on the number of robots needed based on polygon symmetry and providing algorithms that work under various models.
Contribution
It proves tight bounds on the number of robots needed for meeting based on polygon symmetry and introduces algorithms that operate under minimal assumptions and initial conditions.
Findings
For polygons with rotational symmetry of order σ, σ+1 robots suffice.
Two robots can meet in polygons whose barycenter is not in a hole.
Algorithms work under various models, including oblivious and memory-based robots.
Abstract
The Meeting problem for searchers in a polygon (possibly with holes) consists in making the searchers move within , according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of , we minimize the number of searchers for which the Meeting problem is solvable. Specifically, if has a rotational symmetry of order (where corresponds to no rotational symmetry), we prove that searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes).…
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Taxonomy
TopicsOptimization and Search Problems · Modular Robots and Swarm Intelligence · Robotics and Sensor-Based Localization
