Coarse-Grained Parallelization of Cellular-Automata Simulation Algorithms

  • Olga Bandman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4671)


Simulating spatial dynamics in physics by Cellular Automata (CA) requires very large computation power, and, hence, CA simulation algorithms are to be implemented on multiprocessors. The preconceived opinion, that no much effort is required to obtain highly efficient coarse grained parallel CA algorithm, is not always true. In fact, a great variety of CA modifications coming into practical use need appropriate, sometimes sophisticated, methods of CA algorithms parallel implementation. Proceeding from the above a general approach to CA parallelization, based on domain decomposition correctness conditions, is formulated. Starting from the correctness conditions particular parallelization methods are developed for the main classes of CA simulation models: synchronous CA with multi-cell updating rules, asynchronous probabilistic CA, and CA compositions. Examples and experimental results are given for each case.


Cellular Automaton Domain Decomposition Cellular Automaton Parallel Implementation Correctness Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Toffolli, T.: Cellular Automata as an Alternative to (rather than Approximation of) Differential Equations in Modeling Physics. Physica D 10, 117–127 (1984)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Wolfram, S.: A new kind of science. Wolfram Media Inc., Champaign, Ill., USA (2002)Google Scholar
  3. 3.
    Toffolli, T., Margolus, N.: Cellular Automata Machines. MIT Press, Cambridge (1987)Google Scholar
  4. 4.
    Rothman, B.H., Zaleski, S.: Lattice-Gas Cellular Automata. Cambridge Univ. Press, Complex Hydrodynamics. London (1997)zbMATHGoogle Scholar
  5. 5.
    Latkin, E.I., Elokhin, V.I., Gorodetskii, V.V.: Spiral concentration waves in the Monte-Carlo model of CO oxidation over Pd(110) caused by synchronization via COads diffusion between separate parts of catalytic surface. Chemical Engineering Journal 91, 123–131 (2003)CrossRefGoogle Scholar
  6. 6.
    Neizvestny, I.G., Shwartz, N.L., Yanovitskaya, Z.S., Zverev, A.V.: 3D-model of epitaxial growth on porous {111} and {100} Si surfaces. Computer Physics Communications 147, 272–275 (2002)zbMATHCrossRefGoogle Scholar
  7. 7.
    Sipper, M.: Evolution of Parallel Cellular Machines: The Cellular Programming Approach. Springer, Heidelberg (1997)Google Scholar
  8. 8.
    Bandini, S., Erbacci, G., Mauri, G.: Implementing Cellular Automata Based Models on Parallel Architectures: The CAPP Project. In: Malyshkin, V. (ed.) Parallel Computing Technologies. LNCS, vol. 1662, pp. 167–179. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Carotenuto, L., Mele, F., Furnari, M.M., Napolitano, R.: Pecans: A parallel environment for cellular automata modeling. Complex Systems 10, 23–41 (1996)zbMATHGoogle Scholar
  10. 10.
    Malinetski, G.G., Stepantsov, M.E.: Modeling Diuffusive Processes by Cellular Automata with Margolus Neighborhood. Zhurnal Vychislitelnoy Matematiki i Matematicheskoy Phiziki (in Russian) 36(6), 1017–1021 (1998)Google Scholar
  11. 11.
    Bandman, O.: Simulation Spatial Dynamics by Probabilistic Cellular Automata. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 10–19. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Achasova, S., Bandman, O., Markova, V., Piskunov, S.: Parallel Substitution Algorithm. In: Theory and Application, World Scientific, Singapore (1994)Google Scholar
  13. 13.
    Park, J.K., Steiglitz, K., Thurston, W.P.: Soliton-like behavior in automata. Physica D 19, 423–432 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Medvedev, Y.G.: Experimental study of Computational characteristic of parallel implementation of 3D cellular Automata model of viscous flow. In: Proceedings of Scientific Confernce Parallel Programming Technology, pp. 79–82. Moscow Univ. Press (2006)Google Scholar
  15. 15.
    Bandman, O.: Parallel Implementation of Asynchronous Cellular Automata Algorithm. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 41–47. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Nedea, S.V., Lukkien, J.J., Jansen, A.P.J., Hilbers, P.A.J.: Methods for parallel simulation of surface reaction. In: Werner, B. (ed.) 4th Int. Workshop on Parallel and Distributrd Scientific and Engineering Computing with Applications, pp. 7–16. IEEE Comp. Society, Nice, France (2003)Google Scholar
  17. 17.
    Chen, N., Glazier, J.A., Alber, M.S.A: A Parallel Implementation of the Cellular Potts Model for Simulation of Cell-Based Morphogenesis. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 58–67. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Bandman, O.: Composing Fine-graned Parallel Algorithms for Spatial Dynamics Simulation. In: Malyshkin, V. (ed.) PaCT 2005. LNCS, vol. 3606, pp. 99–113. Springer, Heidelberg (2005)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Olga Bandman
    • 1
  1. 1.Supercomputer Software Department, ICM&MG, Siberian Branch, Russian Academy of Sciences, Pr. Lavrentieva, 6, Novosibirsk, 630090Russia

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