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Significant work has been done on computing the ``average'' optimal solution value for various $\mathsf{NP}$-complete problems using the Erd\"{o}s-R\'{e}nyi model to establish \emph{critical thresholds}. Critical thresholds define narrow bounds for the optimal solution of a problem instance such that the probability that the solution value lies outside these bounds vanishes as the instance size approaches infinity. In this paper, we extend the Erd\"{o}s-R\'{e}nyi model to general hypergraphs on $n$ vertices and $M$ hyperedges. We consider the problem of determining critical thresholds for the largest cardinality matching, and we show that for $M=o(1.155^n)$ the size of the maximum cardinality matching is almost surely 1. On the other hand, if $M=\Theta(2^n)$ then the size of the maximum cardinality matching is $\Omega(n^{\frac12-\gamma})$ for an arbitrary $\gamma >0$. Lastly, we address the gap where $\Omega(1.155^n)=M=o(2^n)$ empirically through computer simulations.

In the context of satellite monitoring of the earth, we can assume that the surface of the earth is divided into a set of regions. We assume that the impact of a big social/environmental event spills into neighboring regions. Using Identifying Code Sets (ICSes), we can deploy sensors in such a way that the region in which an event takes place can be uniquely identified, even with fewer sensors than regions. As Earth is almost a sphere, we use a soccer ball as a model. We construct a Soccer Ball Graph (SBG), and provide human-oriented, analytical proofs that 1) the SBG has at least 26 ICSes of cardinality ten, implying that there are at least 26 different ways to deploy ten satellites to monitor the Earth and 2) that the cardinality of the minimum Identifying Code Set (MICS) for the SBG is at least nine. We then provide a machine-oriented formal proof that the cardinality of the MICS for the SBG is in fact ten, meaning that one must deploy at least ten satellites to monitor the Earth in the SBG model. We also provide machine-oriented proof that there are exactly 26 ICSes of cardinality ten for the SBG., Comment: 22 pages, 5 figures, preprint

Unwanted samples from private source categories in the learning objective of a partial domain adaptation setup can lead to negative transfer and reduce classification performance. Existing methods, such as re-weighting or aggregating target predictions, are vulnerable to this issue, especially during initial training stages, and do not adequately address class-level feature alignment. Our proposed approach seeks to overcome these limitations by delving deeper than just the first-order moments to derive distinct and compact categorical distributions. We employ objectives that optimize the intra and inter-class distributions in a domain-invariant fashion and design a robust pseudo-labeling for efficient target supervision. Our approach incorporates a complement entropy objective module to reduce classification uncertainty and flatten incorrect category predictions. The experimental findings and ablation analysis of the proposed modules demonstrate the superior performance of our proposed model compared to benchmarks.

In this paper, we present methodologies for optimal selection for renewable energy sites under a different set of constraints and objectives. We consider two different models for the site-selection problem - coarse-grained and fine-grained, and analyze them to find solutions. We consider multiple different ways to measure the benefits of setting up a site. We provide approximation algorithms with a guaranteed performance bound for two different benefit metrics with the coarse-grained model. For the fine-grained model, we provide a technique utilizing Integer Linear Program to find the optimal solution. We present the results of our extensive experimentation with synthetic data generated from sparsely available real data from solar farms in Arizona.

This work proposes a robust Partial Domain Adaptation (PDA) framework that mitigates the negative transfer problem by incorporating a robust target-supervision strategy. It leverages ensemble learning and includes diverse, complementary label feedback, alleviating the effect of incorrect feedback and promoting pseudo-label refinement. Rather than relying exclusively on first-order moments for distribution alignment, our approach offers explicit objectives to optimize intra-class compactness and inter-class separation with the inferred source prototypes and highly-confident target samples in a domain-invariant fashion. Notably, we ensure source data privacy by eliminating the need to access the source data during the adaptation phase through a priori inference of source prototypes. We conducted a series of comprehensive experiments, including an ablation analysis, covering a range of partial domain adaptation tasks. Comprehensive evaluations on benchmark datasets corroborate our framework's enhanced robustness and generalization, demonstrating its superiority over existing state-of-the-art PDA approaches.

An important problem in network science is finding an optimal placement of sensors in nodes in order to uniquely detect failures in the network. This problem can be modelled as an identifying code set (ICS) problem, introduced by Karpovsky et al. in 1998. The ICS problem aims to find a cover of a set $S$, s.t. the elements in the cover define a unique signature for each of the elements of $S$, and to minimise the cover's cardinality. In this work, we study a generalised identifying code set (GICS) problem, where a unique signature must be found for each subset of $S$ that has a cardinality of at most $k$ (instead of just each element of $S$). The concept of an independent support of a Boolean formula was introduced by Chakraborty et al. in 2014 to speed up propositional model counting, by identifying a subset of variables whose truth assignments uniquely define those of the other variables. In this work, we introduce an extended version of independent support, grouped independent support (GIS), and show how to reduce the GICS problem to the GIS problem. We then propose a new solving method for finding a GICS, based on finding a GIS. We show that the prior state-of-the-art approaches yield integer-linear programming (ILP) models whose sizes grow exponentially with the problem size and $k$, while our GIS encoding only grows polynomially with the problem size and $k$. While the ILP approach can solve the GICS problem on networks of at most 494 nodes, the GIS-based method can handle networks of up to 21363 nodes; a $\sim 40\times$ improvement. The GIS-based method shows up to a $520\times$ improvement on the ILP-based method in terms of median solving time. For the majority of the instances that can be encoded and solved by both methods, the cardinality of the solution returned by the GIS-based method is less than $10\%$ larger than the cardinality of the solution found by the ILP method., Comment: 8 pages, to appear in the Proceedings of the 32nd International Joint Conference on Artificial Intelligence (IJCAI 2023), paper 4051

Low Earth Orbit (LEO) satellites present a compelling opportunity for the establishment of a global quantum information network. However, satellite-based entanglement distribution from a networking perspective has not been fully investigated. Existing works often do not account for satellite movement over time when distributing entanglement and/or often do not permit entanglement distribution along inter-satellite links, which are two shortcomings we address in this paper. We first define a system model which considers both satellite movement over time and inter-satellite links. We next formulate the optimal entanglement distribution (OED) problem under this system model and show how to convert the OED problem in a dynamic physical network to one in a static logical graph which can be used to solve the OED problem in the dynamic physical network. We then propose a polynomial time greedy algorithm for computing satellite-assisted multi-hop entanglement paths. We also design an integer linear programming (ILP)-based algorithm to compute optimal solutions as a baseline to study the performance of our greedy algorithm. We present evaluation results to demonstrate the advantage of our model and algorithms.

The standard closed-set domain adaptation approaches seek to mitigate distribution discrepancies between two domains under the constraint of both sharing identical label sets. However, in realistic scenarios, finding an optimal source domain with identical label space is a challenging task. Partial domain adaptation alleviates this problem of procuring a labeled dataset with identical label space assumptions and addresses a more practical scenario where the source label set subsumes the target label set. This, however, presents a few additional obstacles during adaptation. Samples with categories private to the source domain thwart relevant knowledge transfer and degrade model performance. In this work, we try to address these issues by coupling variational information and adversarial learning with a pseudo-labeling technique to enforce class distribution alignment and minimize the transfer of superfluous information from the source samples. The experimental findings in numerous cross-domain classification tasks demonstrate that the proposed technique delivers superior and comparable accuracy to existing methods., Comment: Accepted in the 56th Asilomar Conference on Signals, Systems, and Computers, 2022

In contrast to a standard closed-set domain adaptation task, partial domain adaptation setup caters to a realistic scenario by relaxing the identical label set assumption. The fact of source label set subsuming the target label set, however, introduces few additional obstacles as training on private source category samples thwart relevant knowledge transfer and mislead the classification process. To mitigate these issues, we devise a mechanism for strategic selection of highly-confident target samples essential for the estimation of class-importance weights. Furthermore, we capture class-discriminative and domain-invariant features by coupling the process of achieving compact and distinct class distributions with an adversarial objective. Experimental findings over numerous cross-domain classification tasks demonstrate the potential of the proposed technique to deliver superior and comparable accuracy over existing methods.

The Smart Grid System (SGS) is a joint network comprising the power and the communication network. In this paper, the underlying intra-and-interdependencies between entities for a given SGS is captured using a dependency model called Modified Implicative Interdependency Model (MIIM) [1]. Given an integer K, the K-contingency list problem gives the list of K-most critical entities, failure of which maximizes the network damage at the current time. The problem being NP complete [2] and owing to the higher running time of the given Integer Linear Programming (ILP) based solution [3], a much faster heuristic solution to generate an event driven self-updating K-contingency list [4] is also given in this paper. Based on the contingency lists obtained from both the solutions, this paper proposes an adaptive entity hardening technique based on a leader-follower game theoretic approach that arrests the cascading failure of entities in the SGS after an initial failure of entities. The validation of the work is done by comparing the contingency lists using both types of solutions, obtained for different K values using the MIIM model on a smart grid of IEEE 14-Bus system with that obtained by simulating the smart grid using a co-simulation system formed by MATPOWER and Java Network Simulator (JNS). The K-contingency list obtained for a smart grid of IEEE 14-Bus system also indicate that the network damage predicted by both the ILP based solution and heuristic solution using MIIM are more realistic compared to that obtained using another dependency model called Implicative Interdependency Model (IIM) [2]. Advantage of using the MIIM based heuristic solution is also shown in this paper when larger SGS of IEEE 118-Bus is considered. Finally, it is shown how the adaptive hardening helps in improving the network performance., Comment: This paper is accepted for publication in American Journal of Science and Engineering. arXiv admin note: text overlap with arXiv:2101.08896

Smart grid monitoring, automation and control will completely rely on PMU based sensor data soon. Accordingly, a high throughput, low latency Information and Communication Technology (ICT) infrastructure should be opted in this regard. Due to the low cost, low power profile, dynamic nature, improved accuracy and scalability, wireless sensor networks (WSNs) can be a good choice. Yet, the efficiency of a WSN depends a lot on the network design and the routing technique. In this paper a new design of the ICT network for smart grid using WSN is proposed. In order to understand the interactions between different entities, detect their operational levels, design the routing scheme and identify false data injection by particular ICT entities, a new model of interdependency called the Multi State Implicative Interdependency Model (MSIIM) is proposed in this paper, which is an updated version of the Modified Implicative Interdependency Model (MIIM) [1]. MSIIM considers the data dependency and operational accuracy of entities together with structural and functional dependencies between them. A multi-path secure routing technique is also proposed in this paper which relies on the MSIIM model for its functioning. Simulation results prove that MSIIM based False Data Injection (FDI) detection and mitigation works better and faster than existing methods., Comment: 6 pages, Accepted for publication in The IEEE International workshop on Communication, Computing, and Networking in Cyber Physical Systems (CCNCPS 2021)

A reliable decision making by the operator in a smart grid is contingent upon correct analysis of intra-and-interdependencies between its entities and also on accurate identification of the most critical entities at a given point of time. A measurement based self-updating contingency list can provide real-time information to the operator about current system condition which can help the operator to take the required action. In this paper, the underlying intra-and-interdependencies between entities for a given power-communication network is captured using a dependency model called Modified Implicative Interdependency Model (MIIM) [1]. Given an integer K, the event-driven self-updating contingency list problem gives the list of K-most critical entities, failure of which maximizes the network damage at the current time. Owing to the problem being NP complete, a fast heuristic method to generate a real-time contingency list using system measurements is provided here. The validation of the work is done by comparing the contingency list obtained for different K values using the MIIM model on a smart grid of IEEE 14-Bus system with that obtained by simulating the smart grid using a co-simulation system formed by MATPOWER and Java Network Simulator (JNS). The results also indicate that the network damage predicted by both the ILP based solution [2] and the proposed heuristic solution using MIIM are more realistic compared to that obtained using another dependency model called Implicative Interdependency Model (IIM) [3]., Comment: Presented in 2021 IEEE 11th Annual Computing and Communication Workshop and Conference (CCWC). arXiv admin note: substantial text overlap with arXiv:2008.08074

The generalization power of deep-learning models is dependent on rich-labelled data. This supervision using large-scaled annotated information is restrictive in most real-world scenarios where data collection and their annotation involve huge cost. Various domain adaptation techniques exist in literature that bridge this distribution discrepancy. However, a majority of these models require the label sets of both the domains to be identical. To tackle a more practical and challenging scenario, we formulate the problem statement from a partial domain adaptation perspective, where the source label set is a super set of the target label set. Driven by the motivation that image styles are private to each domain, in this work, we develop a method that identifies outlier classes exclusively from image content information and train a label classifier exclusively on class-content from source images. Additionally, elimination of negative transfer of samples from classes private to the source domain is achieved by transforming the soft class-level weights into two clusters, 0 (outlier source classes) and 1 (shared classes) by maximizing the between-cluster variance between them.

Electric power grid components, such as high voltage transformers (HVTs), generating stations, substations, etc. are expensive to maintain and, in the event of failure, replace. Thus, regularly monitoring the behavior of such components is of utmost importance. Furthermore, the recent increase in the number of cyberattacks on such systems demands that such monitoring strategies should be robust. In this paper, we draw inspiration from work in Moving Target Defense (MTD) and consider a dynamic monitoring strategy that makes it difficult for an attacker to prevent unique identification of behavioral signals that indicate the status of HVTs. We first formulate the problem of finding a differentially immune configuration set for an MTD in the context of power grids and then propose algorithms to compute it. To find the optimal movement strategy, we model the MTD as a two-player game and consider the Stackelberg strategy. With the help of IEEE test cases, we show the efficacy and scalability of our proposed approaches., Comment: Accepted to the Conference on Decision and Game Theory for Security (GameSec), 2020

We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset $S^* \subseteq S$ of minimum cardinality such that for each point $p_i \in P$, the subset $S_i^* \subseteq S^*$ covering $p_i$ satisfies $S_i^*\neq \emptyset$, and each pair $p_i,p_j \in P$, $i \neq j$, we have $S_i^* \neq S_j^*$. In the \emph{continuous version} of the problem, the solution set $S^*$ can be chosen freely among a (potentially infinite) class of allowed geometric objects. In the 1-dimensional case ($d=1$), the points in $P$ are placed on a horizontal line $L$, and the objects in $S$ are finite-length line segments aligned with $L$ (called intervals). We show that the discrete version of this problem is NP-complete. This is somewhat surprising as the continuous version is known to be polynomial-time solvable. Still, for the 1-dimensional discrete version, we design a polynomial-time $2$-approximation algorithm. We also design a PTAS for both discrete and continuous versions in one dimension, for the restriction where the intervals are all required to have the same length. We then study the 2-dimensional case ($d=2$) for axis-parallel unit square objects. We show that both continuous and discrete versions are NP-complete, and design polynomial-time approximation algorithms that produce $(16\cdot OPT+1)$-approximate and $(64\cdot OPT+1)$-approximate solutions respectively, using rounding of suitably defined integer linear programming problems. We show that the identifying code problem for axis-parallel unit square intersection graphs (in $d=2$) can be solved in the same manner as for the discrete version of the discriminating code problem for unit square objects.

A smart grid system can be considered as a multi-layered network with power network in one layer and communication network in the other. The entities in both the layers exhibit complex intra-and-interdependencies between them. A reliable decision making by the smart grid operator is contingent upon correct analysis of such dependencies between its entities and also on accurate identification of the most critical entities in the system. The Modified Implicative Interdependency Model (MIIM) [1] successfully captures such dependencies using multi-valued Boolean Logic based equations called Interdependency Relations (IDRs) after most of the existing models made failed attempts in doing that. In this paper, for any given integer K, this model is used to identify the K-most vulnerable entities in a smart grid, failure of which can maximize the network damage. Owing to the problem being NP complete, an Integer Linear Programming (ILP) based solution is given here. Validation of the model [1] and the results of the ILP based solution is done by simulating a smart grid system of IEEE 14-Bus using MATPOWER and Java Network Simulator (JNS). Simulation results prove that not only the model MIIM [1] is correct but also it can predict the network damage for failure of K-most vulnerable entities more accurately than its predecessor Implicative Interdependency Model (IIM) [2]., Comment: 6 pages, 4 figures, Accepted for publication in CommNet 2020

Monitoring and automation of the critical infrastructures like the power grid is improvised by the support of an efficient and secure communication net-work. Due to the low cost, low power profile, dynamic nature, improved ac-curacy and scalability, wireless sensor networks (WSN) became an attractive choice for the Information and Communication Technology (ICT) system of the smart grid. However, the energy efficiency and security of WSN depends highly on the network design and routing scheme. In this paper, a WSN based Secure and Energy Efficient Remote Monitoring Technique (SERMT) is proposed by demonstrating a WSN based ICT network model for perva-sive monitoring of the generation and transmission part of the power network in a smart grid system. The performance of the proposed network model de-signed for a smart grid of IEEE 118-Bus system coupled with the secure routing technique is tested during cyber-attacks by means of NS2 and the simulation results indicate that it performs better than existing smart grid monitoring methods like Lo-ADI [1] with respect to packet drop count and throughput., Comment: 11 pages

The reliable and resilient operation of the smart grid necessitates a clear understanding of the intra-and-inter dependencies of its power and communication systems. This understanding can only be achieved by accurately depicting the interactions between the different components of these two systems. This paper presents a model, called modified implicative interdependency model (MIIM), for capturing these interactions. Data obtained from a power utility in the U.S. Southwest is used to ensure the validity of the model. The performance of the model for a specific power system application namely, state estimation, is demonstrated using the IEEE 118-bus system. The results indicate that the proposed model is more accurate than its predecessor, the implicative interdependency model (IIM) [1], in predicting the system state in case of failures in the power and/or communication systems., Comment: 8 pages. Accepted for publication in SusTech 2020 : 2020 IEEE Conference on Technologies for Sustainability

According to the Center of Disease Control (CDC), the Opioid epidemic has claimed more than 72,000 lives in the US in 2017 alone. In spite of various efforts at the local, state and federal level, the impact of the epidemic is becoming progressively worse, as evidenced by the fact that the number of Opioid related deaths increased by 12.5\% between 2016 and 2017. Predictive analytics can play an important role in combating the epidemic by providing decision making tools to stakeholders at multiple levels - from health care professionals to policy makers to first responders. Generating Opioid incidence heat maps from past data, aid these stakeholders to visualize the profound impact of the Opioid epidemic. Such post-fact creation of the heat map provides only retrospective information, and as a result, may not be as useful for preventive action in the current or future time-frames. In this paper, we present a novel deep neural architecture, which learns subtle spatio-temporal variations in Opioid incidences data and accurately predicts future heat maps. We evaluated the efficacy of our model on two open source datasets- (i) The Cincinnati Heroin Overdose dataset, and (ii) Connecticut Drug Related Death Dataset.

Terrorist attacks all across the world have become a major source of concern for almost all national governments. The United States Department of State's Bureau of Counter-Terrorism, maintains a list of 66 terrorist organizations spanning the entire world. Actively monitoring a large number of organizations and their members, require considerable amounts of resources on the part of law enforcement agencies. Oftentimes, the law enforcement agencies do not have adequate resources to monitor these organizations and their members effectively. On multiple incidences of terrorist attacks in recent times across Europe, it has been observed that the perpetrators of the attack were in the suspect databases of the law enforcement authorities, but weren't under active surveillance at the time of the attack, due to resource limitations on the part of the authorities. As the suspect databases in various countries are very large, and it takes significant amount of technical and human resources to monitor a suspect in the database, monitoring all the suspects in the database may be an impossible task. In this paper, we propose a novel terror network monitoring approach that will significantly reduce the resource requirement of law enforcement authorities, but still provide the capability of uniquely identifying a suspect in case the suspect becomes active in planning a terrorist attack. The approach relies on the assumption that, when an individual becomes active in planning a terrorist attack, his/her friends/associates will have some inkling of the individuals plan. Accordingly, even if the individual is not under active surveillance by the authorities, but the individual's friends/associates are, then the individual planning the attack can be uniquely identified. We apply our techniques on various real-world terror network datasets and show the effectiveness of our approach.

High voltage power transformers are one of the most critical equipments in the electric power grid. A sudden failure of a power transformer can significantly disrupt bulk power delivery. Before a transformer reaches its critical failure state, there are indicators which, if monitored periodically, can alert an operator that the transformer is heading towards a failure. One of the indicators is the signal to noise ratio (SNR) of the voltage and current signals in substations located in the vicinity of the transformer. During normal operations, the width of the SNR band is small. However, when the transformer heads towards a failure, the widths of the bands increase, reaching their maximum just before the failure actually occurs. This change in width of the SNR can be observed by sensors, such as phasor measurement units (PMUs) located nearby. Identifying Code is a mathematical tool that enables one to uniquely identify one or more {\em objects of interest}, by generating a unique signature corresponding to those objects, which can then be detected by a sensor. In this paper, we first describe how Identifying Code can be utilized for detecting failure of power transformers. Then, we apply this technique to determine the fewest number of sensors needed to uniquely identify failing transformers in different test systems.

Opioid overdose has emerged as a full blown epidemic in the United States. In the last few years, there has been an alarming increase in Opioid related deaths, resulting in the loss of 63,600 lives in 2016 alone. The epidemic which is killing more than 100 people each day, was declared as a public health emergency by the US government, in October 2017. Although a few health related companies and commercial firms have examined this important issue from various available data sources, to the best of our knowledge, the academic community has not been engaged in research in this important topic. It can be safely noted that the study of the epidemic, from the data analytics perspective, is in its infancy. Given that a significant amount of Opioid related data is available in public domain, it provides the academic community an opportunity to analyze such data to provide recommendations to the public health authorities to mitigate the impact of the epidemic. In that vein, we collected some publicly available data to analyze the important contributing factors of the epidemic. In particular, we examine the role of the individuals prescribing Opioid drugs on the spread of the epidemic. In addition, we examine the impact of income level, age and educational level of various neighborhoods in a large US city, on Opioid related incidences, to find any correlation between them., Comment: 5 Pages

A major portion of postings on social networking sites constitute high quality digital images and videos. These images and videos require a fairly large amount of bandwidth during transmission. Accordingly, high quality image and video postings become a challenge for the network service provider, especially in a crowded environment where bandwidth is in high demand. In this paper we present a user satisfaction driven bandwidth allocation scheme for image transmission in such environments. In an image, there are always objects that stand out more than others. The reason behind some set of objects being more important in a scene is based on a number of visual, as well as, cognitive factors. Being motivated by the fact that user satisfaction is more dependent on the quality of these salient objects in an image than non-salient ones, we propose a quantifiable metric for measuring user-satisfiability (based on image quality and delay of transmission). The bandwidth allocation technique proposed thereafter, ensures that this user-satisfiability is maximized. Unlike the existing approaches that utilize some fixed set of non-linear functions for framing the user-satisfiability index, our metric is modelled over customer survey data, where the unknown parameters are trained with machine learning methods., Comment: 7 Pages

Smart grid systems are composed of power and communication network components. The components in either network exhibit complex dependencies on components in its own as well as the other network to drive their functionality. Existing, models fail to capture these complex dependencies. In this paper, we restrict to the dependencies in the power network and propose the Multi-scale Implicative Interdependency Relation (MIIR) model that address the existing limitations. A formal description of the model along with its working dynamics and a brief validation with respect to the 2011 Southwest blackout are provided. Utilizing the MIIR model, the $K$ Contingency List problem is proposed. For a given time instant, the problem solves for a set of $K$ entities in a power network which when failed at that time instant would cause the maximum number of entities to fail eventually. Owing to the problem being NP-complete we devised a Mixed Integer Program (MIP) to obtain the optimal solution and a polynomial time sub-optimal heuristic. The efficacy of the heuristic with respect to the MIP is compared by using different bus system data. In general, the heuristic is shown to provide near optimal solution at a much faster time than the MIP.

The critical infrastructures of the nation such as the power grid and the communication network are highly interdependent. Also, it has been observed that there exists complex interdependent relationships between individual entities of the power grid and the communication network that further obfuscates the analysis, and mitigation of faults in such multi-layered networks. In recent years, the research community has made significant efforts towards gaining insight and understanding of the interdependency relations in such multi-layered networks, and accordingly, a number of models have been proposed and analyzed towards realizing this goal. In this chapter we study existing interdependency models proposed in the recent literature and discuss their approach, and inherent features, towards modeling interdependent multi-layer networks. We also provide a brief discussion into the drawbacks of each of these models and propose an alternate model that addresses these drawbacks by capturing the interdependency relationships using a combination of conjunctive and disjunctive relations.

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., Comment: CRITIS 2016

Critical Infrastructures like power and communication networks are highly interdependent on each other for their full functionality. Many significant research have been pursued to model the interdependency and failure analysis of these interdependent networks. However, most of these models fail to capture the complex interdependencies that might actually exist between the infrastructures. The \emph{Implicative Interdependency Model} that utilizes Boolean Logic to capture complex interdependencies was recently proposed which overcome the limitations of the existing models. A number of problems were studies based on this model. In this paper we study the \textit{Robustness} problem in Interdependent Power and Communication Network. The robustness is defined with respect to two parameters $K \in I^{+} \cup \{0\}$ and $\rho \in (0,1]$. We utilized the \emph{Implicative Interdependency Model} model to capture the complex interdependency between the two networks. The model classifies the interdependency relations into four cases. Computational complexity of the problem is analyzed for each of these cases. A polynomial time algorithm is designed for the first case that outputs the optimal solution. All the other cases are proved to be NP-complete. An in-approximability bound is provided for the third case. For the general case we formulate an Integer Linear Program to get the optimal solution and a polynomial time heuristic. The applicability of the heuristic is evaluated using power and communication network data of Maricopa County, Arizona. The experimental results showed that the heuristic almost always produced near optimal value of parameter $K$ for $\rho < 0.42$., Comment: CRITIS 2015

The power and communication networks are highly interdependent and form a part of the critical infrastructure of a country. Similarly, dependencies exist within the networks itself. It is essential to have a model which captures these dependencies precisely. Previous research has proposed certain models but these models have certain limitations. The limitations of the aforementioned models have been overcome by the Implicative Interdependency Model, which uses Boolean Logic to denote the dependencies. This paper formulates the Entity Hardening problem and the Targeted Entity Hardening problem using the Implicative Interdependency Model. The Entity Hardening problem describes a situation where an operator, with a limited budget, must decide which entities to harden, which in turn would minimize the damage, provided a set of entities fail initially. The Targeted Entity Hardening problem is a restricted version of the Entity Hardening problem. This problem presents a scenario where, the protection of certain entities is of higher priority. If these entities were to be nonfunctional, the economic and societal damage would be higher when compared to other entities being nonfunctional. It has been shown that both problems are NP-Complete. An Integer Linear Program (ILP) has been devised to find the optimal solution. A heuristic has been described whose accuracy is found by comparing its performance with the optimal solution using real-world and simulated data., Comment: The previous version was made into a journal paper that contains the previous problem along with an existing problem. As the previous version is not intended to be published hence it is requested that this new version is accepted

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., Comment: 7 pages, 5 figures

Efficient communication between nodes in ad-hoc networks can be established through repeated cluster formations with designated \textit{cluster-heads}. In this context minimum d-hop dominating set problem was introduced for cluster formation in ad-hoc networks and is proved to be NP-complete. Hence, an exact solution to this problem for certain subclass of graphs (representing an ad-hoc network) can be beneficial. In this short paper we perform computational complexity analysis of minimum d-hop dominating set problem for directed graphs with in-degree bounded by $1$. The optimum solution of the problem can be found polynomially by exploiting certain properties of the graph under consideration. For a digraph $G_{D}=(V_D,E_D)$ an $\mathcal{O}(|V_D|^2)$ solution is provided to the problem.

Mobility pattern of nodes in a mobile network has significant impact on the connectivity properties of the network. One such mobile network that has drawn attention of researchers in the past few years is the Airborne Networks (AN) due to its importance in civil and military purpose and due to the several complex issues in these domains. Since the nodes in an airborne network (AN) are heterogeneous and mobile, the design of a reliable and robust AN is highly complex and challenging. In this paper a persistent backbone based architecture for an AN has been considered where a set of airborne networking platforms (ANPs - aircrafts, UAVs and satellites) form the backbone of the AN. End to end connectivity of the backbone nodes is crucial in providing the communication among the hosts. Since ANPs are prone to failure because of attacks like EMP attack or jamming, another important issue is to improve the robustness of the backbone network against these attacks. Such attacks will impact specific geographic regions at specific times and if an ANP is within the fault region during the time of attack, it will fail. This paper focuses on connectivity and fault-tolerance issues in ANs and studies algorithms to compute the minimum transmission range of ANPs in fault free and faulty scenarios to ensure network connectivity all the times. It also considers the scenario where the network may have to operate in a disconnected mode for some part of time and data transmissions may be tolerant to some amount of delay. Hence, ANPs may not need to have end-to-end paths all the time but they should be able to transmit data to each other within bounded time., Comment: The section on Computation of Critical Transmission Range In Faculty Scenario has been published in proceedings of Milcom 2011: S. Shirazipourazad, P. Ghosh and A. Sen, On Connectivity of Airborne Networks in Presence of Region-based Faults, IEEE Milcom, Military Communications Conference, Baltimore, MD, 2011

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., Comment: 6 pages, 4 figures, submitted to NetSciCom 2014

Computational complexity of the design problem for a network with a target value of Region-Based Component Decomposition Number (RBCDN) has been proven to be NP-complete.

The U.S. Air Force currently is in the process of developing an Airborne Network (AN) to provide support to its combat aircrafts on a mission. The reliability needed for continuous operation of an AN is difficult to achieve through completely infrastructure-less mobile ad hoc networks. In this paper we first propose an architecture for an AN where airborne networking platforms (ANPs - aircrafts, UAVs and satellites) form the backbone of the AN. In this architecture, the ANPs can be viewed as mobile base stations and the combat aircrafts on a mission as mobile clients. The combat aircrafts on a mission move through a space called air corridor. The goal of the AN design is to form a backbone network with the ANPs with two properties: (i) the backbone network remains connected at all times, even though the topology of the network changes with the movement of the ANPs, and (ii) the entire 3D space of the air corridor is under radio coverage at all times by the continuously moving ANPs. In addition to proposing an architecture for an AN, the contributions of the paper include, development of an algorithm that finds the velocity and transmission range of the ANPs so that the dynamically changing backbone network remains connected at all times, development of a routing algorithm that ensures a connection between the source-destination node pair with the fewest number of path switching, given the dimensions of the air corridor and the radius of the coverage sphere associated with an ANP, development of an algorithm that finds the fewest number of ANPs required to provide complete coverage of the air corridor at all times, development of an algorithm that provides connected-coverage to the air corridor at all times, and development of a visualization tool that depicts the movement patterns of the ANPs and the resulting dynamic graph and the coverage volume of the backbone network.