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Minimum vertex cover problem for coupled interdependent networks with cascading failures

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  • Veremyev, Alexander
  • Sorokin, Alexey
  • Boginski, Vladimir
  • Pasiliao, Eduardo L.

Abstract

This paper defines and analyzes a generalization of the classical minimum vertex cover problem to the case of two-layer interdependent networks with cascading node failures that can be caused by two common types of interdependence. Previous studies on interdependent networks mainly addressed the issues of cascading failures from a numerical simulations perspective, whereas this paper proposes an exact optimization-based approach for identifying a minimum-cardinality set of nodes, whose deletion would effectively disable both network layers through cascading failure mechanisms. We analyze the computational complexity and linear 0–1 formulations of the defined problems, as well as prove an LP approximation ratio result that generalizes the well-known 2-approximation for the classical minimum vertex cover problem. In addition, we introduce the concept of a “depth of cascade” (i.e., the maximum possible length of a sequence of cascading failures for a given interdependent network) and show that for any problem instance this parameter can be explicitly derived via a polynomial-time procedure.

Suggested Citation

  • Veremyev, Alexander & Sorokin, Alexey & Boginski, Vladimir & Pasiliao, Eduardo L., 2014. "Minimum vertex cover problem for coupled interdependent networks with cascading failures," European Journal of Operational Research, Elsevier, vol. 232(3), pages 499-511.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:3:p:499-511
    DOI: 10.1016/j.ejor.2013.08.008
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    References listed on IDEAS

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    1. Ashwin Arulselvan & Clayton W. Commander & Oleg Shylo & Panos M. Pardalos, 2011. "Cardinality-Constrained Critical Node Detection Problem," Springer Optimization and Its Applications, in: Nalân Gülpınar & Peter Harrison & Berç Rüstem (ed.), Performance Models and Risk Management in Communications Systems, pages 79-91, Springer.
    2. 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.
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    Cited by:

    1. Alexander Veremyev & Konstantin Pavlikov & Eduardo L. Pasiliao & My T. Thai & Vladimir Boginski, 2019. "Critical nodes in interdependent networks with deterministic and probabilistic cascading failures," Journal of Global Optimization, Springer, vol. 74(4), pages 803-838, August.
    2. Chen, Lei & Yue, Dong & Dou, Chunxia, 2019. "Optimization on vulnerability analysis and redundancy protection in interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1216-1226.
    3. Hyunju Lee, 2020. "State-dependent age replacement policy for a system subject to cascading failures," Journal of Risk and Reliability, , vol. 234(2), pages 359-376, April.
    4. Lin Zhang & Jian Lu & Bai-bai Fu & Shu-bin Li, 2018. "A Review and Prospect for the Complexity and Resilience of Urban Public Transit Network Based on Complex Network Theory," Complexity, Hindawi, vol. 2018, pages 1-36, December.
    5. Gusev, Vasily V., 2023. "Set-weighted games and their application to the cover problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 438-450.
    6. Alla Kammerdiner & Alexander Semenov & Eduardo L. Pasiliao, 2023. "Flight from COVID-19: Multiscale and Multilayer Analyses of the Epidemic-Induced Network Adaptations," SN Operations Research Forum, Springer, vol. 4(2), pages 1-22, June.
    7. Vasily V. Gusev, 2021. "Set-weighted games and their application to the cover problem," HSE Working papers WP BRP 247/EC/2021, National Research University Higher School of Economics.

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