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International Workshop on Cellular Automata and Discrete Complex Systems

AUTOMATA 2014: Cellular Automata and Discrete Complex Systems pp 21–30Cite as

Computational Complexity of the Avalanche Problem on One Dimensional Kadanoff Sandpiles

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

Abstract

In this paper we prove that the general avalanche problem AP is in NC  for the Kadanoff sandpile model in one dimension, answering an open problem of [2]. Thus adding one more item to the (slowly) growing list of dimension sensitive problems since in higher dimensions the problem is P-complete (for monotone sandpiles).

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References

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Acknowledgments

This work was partially supported by IXXI (Complex System Institute, Lyon), ANR projects Subtile, Dynamite and QuasiCool (ANR-12-JS02-011-01), Modmad Federation of U. St-Etienne, the French National Research Agency project EMC (ANR-09-BLAN-0164), FONDECYT Grant 3140527, and Núcleo Milenio Información y Coordinación en Redes (ACGO).

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Authors and Affiliations

  1. Laboratoire I3S (UMR 6070 - CNRS), Université Nice Sophia Antipolis, 2000 Route des Lucioles, BP 121, F-06903, Sophia Antipolis Cedex, France

    Enrico Formenti & Kévin Perrot

  2. Université de Lyon - LIP (UMR 5668 - CNRS - ENS de Lyon - Université Lyon 1), 46 allé d’Italie, 69364, Lyon Cedex 7, France

    Kévin Perrot

  3. Universidad de Chile - DII - DIM - CMM (UMR 2807 - CNRS), 2120 Blanco Encalada, Santiago, Chile

    Kévin Perrot

  4. Université de Lyon - GATE LSE (UMR 5824 - CNRS - Université Lyon 2), Site stéphanois, 6 Rue Basse des Rives, 42 023, Saint-etienne Cedex 2, France

    Éric Rémila

Authors
  1. Enrico Formenti
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  2. Kévin Perrot
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  3. Éric Rémila
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Corresponding author

Correspondence to Kévin Perrot .

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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Formenti, E., Perrot, K., Rémila, É. (2015). Computational Complexity of the Avalanche Problem on One Dimensional Kadanoff Sandpiles. 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-18812-6_2

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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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