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.
Highlights
Percolation theory concerns the flow and the diffusion of some quantity on lattices or networks, for instance a disease on a human network or a message in a communication one [1,2,3]
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 investigated the problem of color-avoiding and color-favored percolation on a diluted lattice [14,15,16], i.e., the problem of finding a path that avoids a certain number of colors, associated with vulnerabilities of nodes or links
Summary
Percolation theory concerns the flow and the diffusion of some quantity on lattices or networks, for instance a disease on a human network or a message in a communication one [1,2,3]. It has many applications in the Internet science [4], for instance in the problem of robustness under attack [5], or the resilience after a random failure of nodes and/or links [6]. We shall show that the results of simulations on such diluted lattices are very similar to that obtained on random networks, with the same average connectivity
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