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A large diffusion and small amplification dynamics for density classification on graphs

Author

Listed:
  • Laura Leal

    (Departamento de Ingeniería Matemática, Universidad de Chile, Chile)

  • Pedro Montealegre

    (Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Chile)

  • Axel Osses

    (DIM-CMM (UMI 2807 CNRS), Universidad de Chile, Chile)

  • Ivan Rapaport

    (DIM-CMM (UMI 2807 CNRS), Universidad de Chile, Chile)

Abstract

The density classification problem on graphs consists in finding a local dynamics such that, given a graph and an initial configuration of 0’s and 1’s assigned to the nodes of the graph, the dynamics converge to the fixed point configuration of all 1’s if the fraction of 1’s is greater than the critical density (typically 1/2) and, otherwise, it converges to the all 0’s fixed point configuration. To solve this problem, we follow the idea proposed in [R. Briceño, P. M. de Espanés, A. Osses and I. Rapaport, Physica D 261, 70 (2013)], where the authors designed a cellular automaton inspired by two mechanisms: diffusion and amplification. We apply this approach to different well-known graph classes: complete, regular, star, Erdös–Rényi and Barabási–Albert graphs.

Suggested Citation

  • Laura Leal & Pedro Montealegre & Axel Osses & Ivan Rapaport, 2023. "A large diffusion and small amplification dynamics for density classification on graphs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-16, May.
    • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:05:n:s0129183123500560
    DOI: 10.1142/S0129183123500560
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