# On Auxiliary Entity Allocation Problem in Multi-layered Interdependent Critical Infrastructures

## TL;DR

This paper introduces the Auxiliary Entity Allocation problem to enhance the resilience of interdependent critical infrastructures by strategically adding dependency modifications, providing optimal and heuristic solutions tested on real data.

## Contribution

It formalizes the Auxiliary Entity Allocation problem, proves its NP-completeness, and offers both an optimal ILP solution and a heuristic with near-optimal performance.

## Key findings

- Heuristic deviates 6.75% from optimal on average
- NP-complete problem with real-world data validation
- Heuristic performs well for restricted cases

## Abstract

Operation of critical infrastructures are highly interdependent on each other. Such dependencies causes failure in these infrastructures to cascade on an initial failure event. Owing to this vulnerability it is imperative to incorporate efficient strategies for their protection. Modifying dependencies by adding additional dependency implications using entities (termed as \emph{auxiliary entities}) is shown to mitigate this issue to a certain extent. With this finding, in this article we introduce the Auxiliary Entity Allocation problem. The objective is to maximize protection in Power and Communication infrastructures using a budget in number of dependency modifications using the auxiliary entities. The problem is proved to be NP-complete in general case. We provide an optimal solution using Integer Linear program and a heuristic for a restricted case. The efficacy of heuristic with respect to the optimal is judged through experimentation using real world data sets with heuristic deviating $6.75 \%$ from optimal on average.