On the Entity Hardening Problem in Multi-layered Interdependent Networks
  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. 
Joydeep Banerjee, Arun Das, Chenyang Zhou, Anisha Mazumder and   Arunabha Sen
cs.NI cs.DS