On the Entity Hardening Problem in multi-layered interdependent networks

Abstract

Abstract-The power grid and the communication network are highly interdependent on each other for their well being. In recent times the research community has shown significant interest in modeling such interdependent networks and studying the impact of failures on these networks. Although a number of models have been proposed, many of them are simplistic in nature and fail to capture the complex interdependencies that exist between the entities of these networks. To overcome the limitations, recently an Implicative Interdependency Model that utilizes Boolean Logic, was proposed and a number of problems were studied. In this paper we study the "entity hardening" problem, where by "entity hardening" we imply the ability of the network operator to ensure that an adversary (be it Nature or human) cannot take a network entity from operative to inoperative state. Given that the network operator with a limited budget can only harden k entities, the goal of the entity hardening problem is to identify the set of k entities whose hardening will ensure maximum benefit for the operator, i.e. maximally reduce the ability of the adversary to degrade the network. We show that the problem is solvable in polynomial time for some cases, whereas for others it is NP-complete. We provide the optimal solution using ILP, and propose a heuristic approach to solve the problem. 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.

Identification of the K-most Vulnerable Entities in a Smart Grid System

“…It is important for the operator of a smart grid to identify the most vulnerable entities in the network, even before any kind of failure or damage takes place in the system. An automated system offering identification of KVE in the steady state of a smart grid will help the operator to decide which of the entities in the system should be hardened [3], so that in any case the maximum damage in the smart grid can be avoided. When one or more entities fail in the smart grid system, many other entities fail as a result and this is called cascading failures, and this often might lead to a catastrophe if not arrested in time.…”

Raptor: a network tool for mitigating the impact of spatially correlated failures in infrastructure networks

“…This module will support multi-layer interdependent network modeling utilizing IIM, and implement the techniques proposed for problems studied under the IIM setting, such as (i) identification of the K most vulnerable nodes [23], (ii) root cause analysis of failures [11], (iii) the entity hardening problem [2], (iv) the smallest pseudotarget set identification problem [13], (v) the robustness analysis problem [3], and (vi) progressive recovery from failure in multi-layer interdependent networks [18]. It may be noted that, as of writing this paper this module is currently under development and will be part of the tool upon its completion.…”

A Network Planning and Management Tool for mitigating the impact of spatially correlated failures in infrastructure networks

“…To overcome the limitations of existing models, the authors of [18] have proposed an Implicative Interdependency Model that is able to capture such complex interdependency. Utilizing this model, several problems on multi-layer interdependent networks have been studied, such as (i) identification of the K most vulnerable nodes [18], (ii) root cause analysis of failures [19], (iii) the entity hardening problem [20], (iv) the smallest pseudo-target set identification problem [21], and (v) the robustness analysis problem [22]. This module will support multi-layer network interdependency modeling using the Implicative Interdependency Model, and analysis of multi-layer networks using the techniques proposed in [18][19][20][21][22].…”