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

Michele Giusfredi and Franco Bagnoli
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Michele Giusfredi: Department of Physics and Astronomy and CSDC, University of Florence, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
Franco Bagnoli: Department of Physics and Astronomy and CSDC, University of Florence, via G. Sansone 1, 50019 Sesto Fiorentino, Italy

Future Internet, 2020, vol. 12, issue 8, 1-12

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.

Keywords: percolation; directed percolation; multi-graphs; color-avoiding percolation (search for similar items in EconPapers)
JEL-codes: O3 (search for similar items in EconPapers)
Date: 2020
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