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From Color-Avoiding to Color-Favored Percolation in Diluted Lattices

Author

Listed:
  • Michele Giusfredi

    (Department of Physics and Astronomy and CSDC, University of Florence, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
    All authors contributed equally to this work.)

  • Franco Bagnoli

    (Department of Physics and Astronomy and CSDC, University of Florence, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
    Istituto Nazionale di Fisica Nucleare, sez. Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy
    All authors contributed equally to this work.)

Abstract

We study the problem of color-avoiding and color-favored percolation in a network, i.e., the problem of finding a path that avoids a certain number of colors, associated with vulnerabilities of nodes or links, or is attracted by them. We investigate here regular (mainly directed) lattices with a fractions of links removed (hence the term “diluted”). We show that this problem can be formulated as a self-organized critical problem, in which the asymptotic phase space can be obtained in one simulation. The method is particularly effective for certain “convex” formulations, but can be extended to arbitrary problems using multi-bit coding. We obtain the phase diagram for some problem related to color-avoiding percolation on directed models. We also show that the interference among colors induces a paradoxical effect in which color-favored percolation is permitted where standard percolation for a single color is impossible.

Suggested Citation

  • Michele Giusfredi & Franco Bagnoli, 2020. "From Color-Avoiding to Color-Favored Percolation in Diluted Lattices," Future Internet, MDPI, vol. 12(8), pages 1-12, August.
    • Handle: RePEc:gam:jftint:v:12:y:2020:i:8:p:139-:d:400699
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    References listed on IDEAS

    as
    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    2. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    3. Grassberger, Peter & Yi-Cheng Zhang,, 1996. "“Self-organized” formulation of standard percolation phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(1), pages 169-179.
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