Identification of $\cal K$ Most Vulnerable Nodes in Multi-layered Network Using a New Model of Interdependency

TL;DR

This paper introduces a novel model for complex interdependencies in multi-layered networks like power grids and communication systems, and presents techniques to identify the most vulnerable nodes efficiently.

Contribution

It proposes a new interdependency model capturing complex relations and provides polynomial-time solutions for some cases and an ILP-based method for others to find vulnerable nodes.

Findings

The model captures conjunctive and disjunctive interdependencies.

The problem is polynomial-time solvable in certain cases.

An ILP-based approach effectively identifies vulnerable nodes using real data.

Abstract

The critical infrastructures of the nation including the power grid and the communication network are highly interdependent. Recognizing the need for a deeper understanding of the interdependency in a multi-layered network, significant efforts have been made by the research community in the last few years to achieve this goal. Accordingly a number of models have been proposed and analyzed. Unfortunately, most of the models are over simplified and, as such, they fail to capture the complex interdependency that exists between entities of the power grid and the communication networks involving a combination of conjunctive and disjunctive relations. To overcome the limitations of existing models, we propose a new model that is able to capture such complex interdependency relations. Utilizing this model, we provide techniques to identify the $\cal K$ most vulnerable nodes of an interdependent network. We show that the problem can be solved in polynomial time in some special cases, whereas for some others, the problem is NP-complete. We establish that this problem is equivalent to computation of a {\em fixed point} of a multilayered network system and we provide a technique for its computation utilizing Integer Linear Programming. Finally, we evaluate the efficacy of our technique using real data collected from the power grid and the communication network that span the Maricopa County of Arizona.