On hardening problems in critical infrastructure systems

Joydeep Banerjee, Kaustav Basu, Arunabha Sen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The power and communication networks are highly interdependent and form a part of the critical infrastructure of a country. Similarly, dependencies exist within the networks itself. It is essential to have a model which captures these dependencies precisely. Previous research has proposed certain models but these models have certain limitations. The limitations of the aforementioned models have been overcome by the Implicative Interdependency Model, which uses Boolean Logic to denote the dependencies. This paper formulates the Entity Hardening problem and the Targeted Entity Hardening problem using the Implicative Interdependency Model. The Entity Hardening problem describes a situation where an operator, with a limited budget, must decide which entities to harden, which in turn would minimize the damage, provided a set of entities fail initially. The Targeted Entity Hardening problem is a restricted version of the Entity Hardening problem. This problem presents a scenario where, the protection of certain entities is of higher priority. If these entities were to be nonfunctional, the economic and societal damage would be higher when compared to other entities being nonfunctional. It has been shown that both problems are NP-Complete. An Integer Linear Program (ILP) has been devised to find the optimal solution. A heuristic has been described whose accuracy is found by comparing its performance with the optimal solution using real-world and simulated data.

Original languageEnglish (US)
Pages (from-to)49-67
Number of pages19
JournalInternational Journal of Critical Infrastructure Protection
StatePublished - Dec 2018


  • Communication network
  • Critical infrastructure
  • Dependency
  • Entity hardening
  • Interdependency
  • Power network
  • Targeted entity hardening

ASJC Scopus subject areas

  • Modeling and Simulation
  • Safety, Risk, Reliability and Quality
  • Computer Science Applications
  • Information Systems and Management


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