A Self-organized Criticality Method for the Study of Color-Avoiding Percolation

Giusfredi, Michele; Bagnoli, Franco

doi:10.1007/978-3-030-34770-3_16

Cited by 2 publications

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“…The color-avoiding percolation (CAP) theory is a recent generalization of the percolation theory, useful to treat these problems [14][15][16][17]. Every node of the network is marked with a one or more colors, associated with the possible vulnerabilities.…”

Section: Introductionmentioning

confidence: 99%

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

Giusfredi

Bagnoli

2020

Future Internet

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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.

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Section: Introductionmentioning

confidence: 99%

“…Acknowledgments: The present version is an extension of Ref. [17]. In this version we added more results on color-avoiding percolation, and the part about color-favored percolation.…”

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confidence: 99%

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

Giusfredi

Bagnoli

2020

Future Internet

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Color-avoiding percolation and branching processes

Fekete,

Molontay,

Ráth

et al. 2024

J. Appl. Probab.

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We study a variant of the color-avoiding percolation model introduced by Krause et al., namely we investigate the color-avoiding bond percolation setup on (not necessarily properly) edge-colored Erdős–Rényi random graphs. We say that two vertices are color-avoiding connected in an edge-colored graph if, after the removal of the edges of any color, they are in the same component in the remaining graph. The color-avoiding connected components of an edge-colored graph are maximal sets of vertices such that any two of them are color-avoiding connected. We consider the fraction of vertices contained in color-avoiding connected components of a given size, as well as the fraction of vertices contained in the giant color-avoidin g connected component. It is known that these quantities converge, and the limits can be expressed in terms of probabilities associated to edge-colored branching process trees. We provide explicit formulas for the limit of the fraction of vertices contained in the giant color-avoiding connected component, and we give a simpler asymptotic expression for it in the barely supercritical regime. In addition, in the two-colored case we also provide explicit formulas for the limit of the fraction of vertices contained in color-avoiding connected components of a given size.

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A Self-organized Criticality Method for the Study of Color-Avoiding Percolation

Cited by 2 publications

References 8 publications

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

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

Color-avoiding percolation and branching processes

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