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Systolic Dissemination in the Arrowhead Family

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Cellular Automata (ACRI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8751))

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Abstract

Although cellular automata (CA) are usually driven by a local rule, global communications are often needed either to synchronize a process or to share common data. However, these communications must be carried out from the nearest-neighbor, local transition. Such disseminations are named “systolic” herein: this metaphor is borrowed from the eponymous cellular architectures. The core of this study is the topology of the “arrowhead” family underlying the CA network in the hexagonal tessellation. The graphs of this family, directed or undirected, are Cayley graphs, or graphs of groups and are therefore vertex-transitive. As a consequence, the local rule is the same within the whole network. Two types of dissemination are presented: a (one–to–all) broadcasting and a (all–to–all) gossiping. For each type, a 3–port, directed scheme and a 6–port, undirected scheme are derived from construction. It is shown that the complexity of these algorithms is the graph diameter, either directed or undirected, according to the case study.

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Author information

Authors and Affiliations

  1. INSA - Institut National des Sciences Appliquées, 20 Avenue des Buttes de Coësmes, 35043, Rennes, France

    Dominique Désérable

Authors
  1. Dominique Désérable
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Editor information

Editors and Affiliations

  1. Dept. of Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Krakow, Poland

    Jarosław Wąs

  2. Dept. of Electrical and Computer Engineering, Democritus University of Thrace, 67100, Xanthi, Greece

    Georgios Ch. Sirakoulis

  3. CSAI - Complex Systems and Artificial Intelligence Research Center, University of Milano-Bicocca, 20126, Milan, Italy

    Stefania Bandini

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Désérable, D. (2014). Systolic Dissemination in the Arrowhead Family. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2014. Lecture Notes in Computer Science, vol 8751. Springer, Cham. https://doi.org/10.1007/978-3-319-11520-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-11520-7_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11519-1

  • Online ISBN: 978-3-319-11520-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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