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

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11938))

Abstract

We study the problem of color-avoiding percolation in a network, i.e., the problem of finding a path that avoids a certain number of colors, associated to vulnerabilities of nodes or links.

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. By using the fragment method, we are able to obtain the phase diagram for many problems related to color-avoiding percolation, showing in particular that results obtained for scale-free networks can be recovered using the dilution of the rule on regular lattices.

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References

  1. Bagnoli, F., Palmerini, P., Rechtman, R.: Algorithmic mapping from criticalityto self-organized criticality. Phys. Rev. E 55(4), 3970–3976 (1997). https://doi.org/10.1103/PhysRevE.55.3970. https://link.aps.org/doi/10.1103/PhysRevE.55.3970

    Article  Google Scholar 

  2. Bagnoli, F., Bellini, E., Massaro, E., Rechtman, R.: Percolation and internet science. Future Internet 11(2), 35 (2019). https://doi.org/10.3390/fi11020035

    Article  Google Scholar 

  3. Bak, P., Sneppen, K.: Punctuated equilibrium and criticality in a simple modelof evolution. Phys. Rev. Lett. 71(24), 4083–4086 (1993). https://doi.org/10.1103/PhysRevLett.71.4083. https://link.aps.org/doi/10.1103/PhysRevLett.71.4083

    Article  Google Scholar 

  4. Kadović, A., Krause, S.M., Caldarelli, G., Zlatic, V.: Bond and site color-avoiding percolation in scale-free networks. Phys. Rev. E 98(6), 062308 (2018). https://doi.org/10.1103/PhysRevE.98.062308. https://link.aps.org/doi/10.1103/PhysRevE.98.062308

    Article  Google Scholar 

  5. Grassberger, P., Zhang, Y.C.: Self-organized formulation of standard percolation phenomena. Phys. A 224(1), 169–179 (1996). https://doi.org/10.1016/0378-4371(95)00321-5. http://www.sciencedirect.com/science/article/pii/0378437195003215, dynamics of Complex Systems

    Article  Google Scholar 

  6. Krause, S.M., Danziger, M.M., Zlatić, V.: Hidden connectivity in networks with vulnerable classes of nodes. Phys. Rev. X 6(4), 041022 (2016). https://doi.org/10.1103/PhysRevX.6.041022

    Article  Google Scholar 

  7. Krause, S.M., Danziger, M.M., Zlatić, V.: Color-avoiding percolation. Phys. Rev. E 96(2), 022313 (2017). https://doi.org/10.1103/PhysRevE.96.022313

    Article  Google Scholar 

  8. Wilkinson, D., Willemsen, J.F.: Invasion percolation: a new form of percolation theory. J. Phys. A: Math. Gen. 16(14), 3365–3376 (1983). https://doi.org/10.1088/0305-4470/16/14/028

    Article  MathSciNet  Google Scholar 

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Correspondence to Franco Bagnoli .

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Giusfredi, M., Bagnoli, F. (2019). A Self-organized Criticality Method for the Study of Color-Avoiding Percolation. In: El Yacoubi, S., Bagnoli, F., Pacini, G. (eds) Internet Science. INSCI 2019. Lecture Notes in Computer Science(), vol 11938. Springer, Cham. https://doi.org/10.1007/978-3-030-34770-3_16

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  • DOI: https://doi.org/10.1007/978-3-030-34770-3_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34769-7

  • Online ISBN: 978-3-030-34770-3

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