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Brief Announcement: Optimal Uniform Circle Formation by Asynchronous Luminous Robots

Authors Caterina Feletti , Debasish Pattanayak , Gokarna Sharma

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  • Theory of computation → Distributed algorithms
Keywords
  • Uniform Circle Formation
  • Robots with Lights
  • Autonomous Robots
  • Rank Encoding
  • Time and Color Complexities
  • Computational SEC

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Abstract

We study the Uniform Circle Formation (UCF) problem for a swarm of n autonomous mobile robots operating in Look-Compute-Move (LCM) cycles on the Euclidean plane. We assume our robots are luminous, i.e. equipped with a persistent light that can assume a color chosen from a fixed palette, and opaque, i.e. not able to see beyond a collinear robot. Robots are said to collide if they share positions or their paths intersect within concurrent LCM cycles. To solve UCF, a swarm of n robots must autonomously arrange themselves so that each robot occupies a vertex of the same regular n-gon not fixed in advance. In terms of efficiency, the goal is to design an algorithm that optimizes (or provides a tradeoff between) two fundamental performance metrics: (i) the execution time and (ii) the size of the color palette.
In this paper, we develop a deterministic algorithm solving UCF avoiding collisions in O(1)-time with O(1) colors under the asynchronous scheduler, which is asymptotically optimal with respect to both time and number of colors used, the first such result. Furthermore, the algorithm proposed here minimizes for the first time what we call the computational SEC, i.e. the smallest circular area where robots operate throughout the whole algorithm.

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Caterina Feletti, Debasish Pattanayak, and Gokarna Sharma. Brief Announcement: Optimal Uniform Circle Formation by Asynchronous Luminous Robots. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 46:1-46:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.46

Author Details

Caterina Feletti
  • Department of Computer Science, Università degli Studi di Milano, Italy
Debasish Pattanayak
  • School of Computer Science, Carleton University, Ottawa, Canada
Gokarna Sharma
  • Department of Computer Science, Kent State University, OH, USA

Acknowledgements

C. Feletti is member of the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (GNCS-INdAM).

References

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