Informatics and Applications
2015, Volume 9, Issue 3, pp 65-71
FOREST FIRE ON A CONFIGURATION GRAPH WITH RANDOM FIRE PROPAGATION
Abstract
The paper considers a random process of fire propagation over links of two types of configuration graphs with random node degrees. Node degrees follow either a power law or the Poisson distribution. The process takes place in a random environment where the probabilities of fire propagation follow the standard uniform distribution.
The optimal values of the node degree distribution parameters that ensure maximum node survival in case of a fire were estimated. The results were obtained for two cases of fire start: targeted start - when a fire starts from the node with the highest degree and random ignition - when a fire starts from an equiprobably chosen node. A comparative analysis of two graph models (power law and Poisson) in terms of the number of nodes remained after the fire was performed.
[+] References (17)
- Cohen, R., K. Erez, D. Ben-Avraham, and S. Havlin. 2000. Resilience of the Internet to random breakdowns. Phys. Rev. Lett. 85:4626-4628.
- Bollobas, B., and O. Riordan. 2004. Robustness and vulnerability of scale-free random graphs. Internet Math. 1(1):1-35.
- Durrett, R. 2007. Random graph dynamics. Cambridge: Cambridge University Press. 221 p.
- Hofstad, R. 2011. Random graphs and complex networks. Eindhoven: Eindhoven University of Technology. 363 p.
- Drossel, B., and F Schwabl. 1992. Self-organized critical forest-fire model. Phys. Rev. Lett. 69:1629-1632.
- Bertoin, J. 2011. Burning cars in a parking lot. Commun. Math. Phys. 306:261-290.
- Bertoin, J. 2012. Fires on trees. Annales de I'Institut Henri Poincare Probabilites et Statistiques 48(4):909-921.
- Arinaminparty, N., S. Kapadia, and R. May. 2012. Size and complexity model financial systems. Proc. Natl. Acad. Sci. USA 109:18338-18343.
- Leri, M.M., and Yu. L. Pavlov. 2013. Lesnoy pozhar na sluchaynom grafe so sgoraemymi rebrami [Forest fire on random graph with inflammable links]. Uchenye Zapis- ki PetrGU. Estestvennye i tekhnicheskie nauki ser. [Proceedings of Petrozavodsk State University. Natural and engeneering sciences ser.] 2(131):96-99.
- Leri, M., and Yu. Pavlov. 2013. Power-law graphs robustness and forest fires. 10th Conference (International) "Computer Data Analysis and Modeling: Theoretical and Applied Stochastics" Proceedings, Minsk. 1:74-77.
- Leri, M., and Yu. Pavlov. 2014. Power-law random graphs' robustness: Link saving and forest fire model. Austrian J. Stat. 43(4):229-236.
- Bollobas, B. A. 1980. A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. Eur. J. Combust. 1:311-316.
- Faloutsos, C., P Faloutsos, and M. Faloutsos. 1999. On power-law relationships of the internet topology. Comp. Comm. Rev. 29:251-262.
- Reittu, H., and I. Norros 2004. On the power-law random graph model of massive data networks. Perform. Evaluation 55:3-23.
- Tangmunarunkit, H., R. Govindan, S. Jamin, S. Shenker, and W. Willinger. 2002. Network topology generators: Degree-based vs. structural. SIGC0MM'02 Proceedings. Pittsburgh, USA. 147-159.
- Matsumoto, M., and T. Nishimura. 1998. Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. Modeling Comput. Simul. 8(1):3-30.
- Leri, M., and Yu. Pavlov. 2014. Forest fire models on configuration random graphs. 3rd Russian Finnish Symposium on Discrete Mathematics: Extended Abstracts. Petrozavodsk. 68-70.
[+] About this article
Title
FOREST FIRE ON A CONFIGURATION GRAPH WITH RANDOM FIRE PROPAGATION
Journal
Informatics and Applications
2015, Volume 9, Issue 3, pp 65-71
Cover Date
2015-02-30
DOI
10.14357/19922264150307
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
configuration graphs; power-law distribution; Poisson distribution; robustness; forest fire model
Authors
M. M. Leri 
Author Affiliations
Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Russian Federation
|