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Finding minimum node separators: A Markov chain Monte Carlo method

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  • Lee, Joohyun
  • Kwak, Jaewook
  • Lee, Hyang-Won
  • Shroff, Ness B.

Abstract

In networked systems such as communication networks or power grids, graph separation from node failures can damage the overall operation severely. One of the most important goals of network attackers is thus to separate nodes so that the sizes of connected components become small. In this work, we consider the problem of finding a minimum α-separator, that partitions the graph into connected components of sizes at most αn, where n is the number of nodes. To solve the α-separator problem, we develop a random walk algorithm based on Metropolis chain. We characterize the conditions for the first passage time (to find an optimal solution) of our algorithm. We also find an optimal cooling schedule, under which the random walk converges to an optimal solution almost surely. Furthermore, we generalize our algorithm to non-uniform node weights. We show through extensive simulations that the first passage time is less than O(n3), thereby validating our analysis. The solution found by our algorithm allows us to identify the weakest points in the network that need to be strengthened. Simulations in real topologies show that attacking a dense area is often not an efficient solution for partitioning a network into small components.

Suggested Citation

  • Lee, Joohyun & Kwak, Jaewook & Lee, Hyang-Won & Shroff, Ness B., 2018. "Finding minimum node separators: A Markov chain Monte Carlo method," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 225-235.
  • Handle: RePEc:eee:reensy:v:178:y:2018:i:c:p:225-235
    DOI: 10.1016/j.ress.2018.06.005
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    1. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    2. Chi Zhang & José Ramirez-Marquez & Claudio Sanseverino, 2011. "A holistic method for reliability performance assessment and critical components detection in complex networks," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 661-675.
    3. V. Rosato & L. Issacharoff & F. Tiriticco & S. Meloni & S. De Porcellinis & R. Setola, 2008. "Modelling interdependent infrastructures using interacting dynamical models," International Journal of Critical Infrastructures, Inderscience Enterprises Ltd, vol. 4(1/2), pages 63-79.
    4. Wang, Xiaolin & Balakrishnan, Narayanaswamy & Guo, Bo, 2014. "Residual life estimation based on a generalized Wiener degradation process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 13-23.
    5. Dunn, Sarah & Wilkinson, Sean, 2017. "Hazard tolerance of spatially distributed complex networks," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 1-12.
    6. Ferrario, E. & Pedroni, N. & Zio, E., 2016. "Evaluation of the robustness of critical infrastructures by Hierarchical Graph representation, clustering and Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 155(C), pages 78-96.
    7. Ramirez-Marquez, Jose E. & Rocco, Claudio M. & Barker, Kash & Moronta, Jose, 2018. "Quantifying the resilience of community structures in networks," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 466-474.
    8. Li, Jian & Dueñas-Osorio, Leonardo & Chen, Changkun & Shi, Congling, 2016. "Connectivity reliability and topological controllability of infrastructure networks: A comparative assessment," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 24-33.
    9. Sergey V. Buldyrev & Roni Parshani & Gerald Paul & H. Eugene Stanley & Shlomo Havlin, 2010. "Catastrophic cascade of failures in interdependent networks," Nature, Nature, vol. 464(7291), pages 1025-1028, April.
    10. S. Özekici & R. Soyer, 2003. "Network reliability assessment in a random environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 574-591, September.
    11. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    12. Compare, M. & Baraldi, P. & Bani, I. & Zio, E. & Mc Donnell, D., 2017. "Development of a Bayesian multi-state degradation model for up-to-date reliability estimations of working industrial components," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 25-40.
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