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Brief Announcement: Mutually-Visible Uniform Circle Formation by Asynchronous Mobile Robots on Grid Plane

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Stabilization, Safety, and Security of Distributed Systems (SSS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13751))

Abstract

In this paper, we consider the Uniform Circle Formation problem, which is a problem to locate all robots uniformly (i.e., with equal central angle) on the circumference of a common circle on infinite grid plane. We first introduce an algorithm to achieve Uniform Circle Formation  using 5 colors with diameter \(\mathcal {O}(N)\), and present another algorithm to achieve Uniform Circle Formation satisfying Complete Visibility (i.e., no three robots are collinear) using 4 colors with diameter \(\mathcal {O}(N^2)\) (optimal) under assumptions such that robots agree on the only one axis, are opaque, operate asynchronously, and do not know the number of robots.

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References

  1. Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

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  2. Flocchini, P., Prencipe, G., Santoro, N. (eds.): Distributed Computing by Mobile Entities, Current Research in Moving and Computing. Lecture Notes in Computer Science, vol. 11340. Springer, Cham (2019)

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  3. R. Adhikary, M.K.Kundu, and B.Sau. Circle formation by asynchronous opaque robots on infinite grid. Comput. Sci. 22(1) (2021)

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Acknowledgements

This work was supported in part by JSPS KAKENHI Grant Numbers 19K11823, 20KK0232, and Foundation of Public Interest of Tatematsu.

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Authors and Affiliations

  1. Nagoya Institute of Technology, Aichi, Japan

    Yoshiaki Ito, Yonghwan Kim & Yoshiaki Katayama

Authors
  1. Yoshiaki Ito
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  2. Yonghwan Kim
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  3. Yoshiaki Katayama
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Corresponding authors

Correspondence to Yoshiaki Ito , Yonghwan Kim or Yoshiaki Katayama .

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Editors and Affiliations

  1. University of Picardie Jules Verne, Amiens, France

    Stéphane Devismes

  2. Sorbonne University, Paris, France

    Franck Petit

  3. Grenoble Alpes University, Saint-Martin-d'Hères, France

    Karine Altisen

  4. Sapienza University of Rome, Rome, Italy

    Giuseppe Antonio Di Luna

  5. IMDEA Networks Institute, Madrid, Spain

    Antonio Fernandez Anta

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Ito, Y., Kim, Y., Katayama, Y. (2022). Brief Announcement: Mutually-Visible Uniform Circle Formation by Asynchronous Mobile Robots on Grid Plane. In: Devismes, S., Petit, F., Altisen, K., Di Luna, G.A., Fernandez Anta, A. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2022. Lecture Notes in Computer Science, vol 13751. Springer, Cham. https://doi.org/10.1007/978-3-031-21017-4_26

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  • DOI: https://doi.org/10.1007/978-3-031-21017-4_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21016-7

  • Online ISBN: 978-3-031-21017-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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