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Generalized FSSP on Hexagonal Tiling: Towards Arbitrary Regular Spaces

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Book cover Cellular Automata and Discrete Complex Systems (AUTOMATA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8996))

Abstract

Here we present a solution to the generalized firing squad synchronization problem that works on some class of shapes in the hexagonal tiling of the plane. The solution is obtained from a previous solution which works on grids with either a von Neumann or a Moore neighborhood. Analyzing the construction of this previous solution, we were able to exhibit a parameter that leads us to abstract the solution. First, and for an arbitrary considered neighborhood, we focus our attention on a class of shapes built from this neighborhood, and determine the corresponding parameter value for them. Second, we apply our previous solution with the determined parameter value for the hexagonal neighborhood and show that, indeed, all the considered shapes on the hexagonal tiling synchronizes.

This work is partially supported by the French program ANR 12 BS02 007 01.

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Authors and Affiliations

  1. LACL, Université Paris-Est-Créteil, Créteil, France

    Luidnel Maignan

  2. LIAFA, Université Paris-Diderot, Paris, France

    Jean-Baptiste Yunès

Authors
  1. Luidnel Maignan
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  2. Jean-Baptiste Yunès
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Corresponding author

Correspondence to Jean-Baptiste Yunès .

Editor information

Editors and Affiliations

  1. University of Hyogo, Himeji, Japan

    Teijiro Isokawa

  2. Hiroshima University, Hiroshima, Japan

    Katsunobu Imai

  3. University of Hyogo, Himeji, Japan

    Nobuyuki Matsui

  4. National Institute of Information and Communications Technology, Osaka, Japan

    Ferdinand Peper

  5. Osaka Electro-Communication University, Osaka, Japan

    Hiroshi Umeo

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Maignan, L., Yunès, JB. (2015). Generalized FSSP on Hexagonal Tiling: Towards Arbitrary Regular Spaces. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2014. Lecture Notes in Computer Science(), vol 8996. Springer, Cham. https://doi.org/10.1007/978-3-319-18812-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-18812-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18811-9

  • Online ISBN: 978-3-319-18812-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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