Smallest pseudo target set identification and related problems using the implicative interdependency model

Critical infrastructures such as the power grid and the communication network form a complex interdependent system where the failure of a small set of entities can trigger a cascading event resulting in the failure of a much larger set of entities. Recognizing the need for a deeper understanding of the interdependence between such critical infrastructures, in the last few years several interdependency models have been proposed and analyzed. However, most of these models are over-simplified and fail to capture the complex interdependencies that may exist in such networks. The more recently proposed Implicative Interdependency Model (IIM) overcomes the limitations of existing models and is able to capture complex relationships that may exist between entities of heterogeneous interdependent networks. In this chapter we outline some of the problems studied using this model and present a detailed study of the Smallest Pseudo Target Set Identification Problem in the IIM setting. We divide the problem into four classes, and show that it is solvable in polynomial time for one class, and is NP-complete for others. We provide an approximation algorithm for the second class, and for the most general class, we provide an optimal solution using an Integer Linear Program, and a heuristic solution. We evaluate the efficacy of our heuristic using power and communication network data of Maricopa County, Arizona. The experiments show that our heuristic almost always produces near optimal results.