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Forest Fire Models on Configuration Random Graphs

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a random process of fire propagation over the links of the two configuration graphs with random node degrees. Node degrees follow either the power-law or the Poisson distribution. A comparative analysis of these graph models in terms of the number of nodes remaining after the fire was performed. The conditions under which this number is greater for one or the other node degree distribution were found.
Wydawca
Rocznik
Strony
313--332
Opis fizyczny
Bibliogr. 18 poz., rys., wykr.
Twórcy
autor
  • Institute of Applied Mathematical Research KRC RAS Petrozavodsk, Russia
autor
  • Institute of Applied Mathematical Research KRC RAS Petrozavodsk, Russia
Bibliografia
  • [1] Bollobas B, Riordan O. Robustness and vulnerability of scale-free random graphs. Internet Mathematics. 2004;1(1):1–35.
  • [2] Cohen R, Erez K, Ben-Avraham D, Havlin S. Resilience of the Internet to Random Breakdowns. Phys Rev Lett. 2000;85:4626–4628.
  • [3] Durrett R. Random Graph Dynamics. Cambridge: Cambridge Univ. Press; 2007.
  • [4] Hofstad R. Random Graphs and Complex Networks. Eindhoven University of Technology; 2011.
  • [5] Bertoin J. Burning cars in a parking lot. Commun Math Phys. 2011;306:261–290.
  • [6] Bertoin J. Fires on trees. Annales de l’Institut Henri Poincare Probabilites et Statistiques. 2012;48(4):909–921.
  • [7] Drossel B, Schwabl F. Self-organized critical forest-fire model. Phys Rev Lett. 1992;69:1629–1632.
  • [8] Arinaminparty N, Kapadia S, May R. Size and complexity model financial systems. Proceedings of the National Academy of Sciences of the USA. 2012;109:18338–18343.
  • [9] Leri M, Pavlov Y. Power-law graphs robustness and forest fires. Proceedings of the 10-th International conference “Computer Data Analysis and Modeling: theoretical and applied stochastics”. 2013;1:74–77.
  • [10] Leri M, Pavlov Y. Power-law random graphs’ robustness: link saving and forest fire model. Austrian Journal of Statistics. 2014;43(4):229–236.
  • [11] Leri MM, Pavlov YL. Forest fire on random graph with inflammable edges. Proc Petrozavodsk State University. 2013;2(131):96–99. In Russian.
  • [12] Bollobas BA. A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. Eur J Comb. 1980;1:311–316.
  • [13] Faloutsos C, Faloutsos P, Faloutsos M. On power-law relationships of the Internet topology. Computer Communications Rev. 1999;29:251–262.
  • [14] Reittu H, Norros I. On the power-law random graph model of massive data networks. Performance Evaluation. 2004;55:3–23.
  • [15] Leri MM. Forest fire on configuration graph with random fire propagation. Informatics and Applications. 2015;9(3):67–73. In Russian.
  • [16] Tangmunarunkit H, Govindan R, Jamin S, Shenker S, Willinger W. Network topology generators: degreebased vs. structural. Proceedings of the SIGCOMM’02. 2002;p. 147–159.
  • [17] Matsumoto M, Nishimura T. Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans on Modeling and Computer Simulation. 1998;8(1):3–30.
  • [18] Norros I, Reittu H. Attack resistance of power-law random graphs in the finite mean, infinite variance region. Internet Mathematics. 2008;5(3):251–266.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e9b21d32-a85a-4ffe-8bf9-d192b670213e
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