Anisha Mazumder

Identification of K most vulnerable nodes in multi-layered network using a new model of interdependency

The critical infrastructures of a 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 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 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.

Progressive Recovery from Failure in Multi-layered Interdependent Network Using a New Model of Interdependency

A number of models have been proposed to analyze interdependent networks in recent years. However most of the models are unable to capture the complex interdependencies between such networks. To overcome the limitations, we have recently proposed a new model. Utilizing this model, we provide techniques for progressive recovery from failure. The goal of the progressive recovery problem is to maximize the system utility over the entire duration of the recovery process. 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 provide two approximation algorithms with performance bounds of 2 and 4 respectively. We provide an optimal solution utilizing Integer Linear Programming and a heuristic. We evaluate the efficacy of our heuristic with both synthetic and real data collected from Phoenix metropolitan area. The experiments show that our heuristic almost always produces near optimal solution.

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 classify the problem into four cases and show that the problem is solvable in polynomial time for the first case, whereas for others it is NP-complete. We provide an inapproximability result for the second case, an approximation algorithm for the third case, and a heuristic for the fourth (general) case. 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.

On the impact of coding parameters on storage requirement of region-based fault tolerant distributed file system design

Advances in technology have resulted in Internet-scale deployment of storage systems such as peer-to-peer storage and cloud storage, where data is distributed over multiple storage nodes in a networked environment. In these environments the storage nodes are often commodity machines and are susceptible to failure. The notion of fault domain, introduced by Microsoft Azure, captures the fault-tolerance aspects of a data center. A fault domain is defined as a set of servers all of which become inaccessible when a single fault (such as the failure of a switch or a router) occurs in the data center. As such a fault domain can be viewed as a spatially correlated or region based failure. In order to enhance reliability through redundancy, maximum distance separable (MDS) codes such as Reed-Solomon codes and (N, K) codings are utilized. In this paper we present analytical results demonstrating that the choice of the coding parameters N and K may have significant impact on storage that will be necessary to achieve reliability. We present a polynomial time algorithm for optimal storage allocation in a mesh network and we conduct extensive experimentation to evaluate the impact of the coding parameters N and K on the storage requirement to provide all region fault tolerance with varying size of the mesh and the fault region.

Region-based fault-tolerant distributed file storage system design in networks

Distributed storage of data files in different nodes of a network enhances its fault tolerance capability by offering protection against node and link failures. Reliability is often achieved through redundancy in one of the following two ways: i storage of multiple copies of the entire file at different locations nodes or ii storage of file segments not entire files at different node locations. In the N,K file distribution scheme, N file segments from a file F are created in such a way that it is possible to reconstruct the entire file, just by accessing any Ki¾?N segments. For the reconstruction scheme to work, it is essential that the K segments of the file are stored in nodes that are connected in the network. However, in the event of node/link failures, the network might become disconnected i.e., split into several connected components. We focus on node failures that are spatially correlated or region based. Such failures are often encountered in disaster situations or natural calamities where only the nodes in the disaster zone are affected. The first goal of this research is to design a least cost file storage scheme to ensure that no matter which region is destroyed; resulting in fragmentation of the network, a largest connected component of the residual network will have enough file segments with which to reconstruct the entire file. In case the least cost to ensure this objective is within the allocated budget, the storage design will be all region fault-tolerant ARFT. In case the least cost exceeds the allocated budget, design of an ARFT file storage system design is impossible. The second goal of this research is to design file storage schemes that will be maximum region fault-tolerant within the allocated budget. The third goal of this research is to investigate the impact of the coding parameters N and K on storage requirements for ensuring all region or \textit{maximum region} fault-tolerant design. We provide maximum region fault-tolerant design. We provide approximation algorithms for the problems and evaluate their performance through simulation using two real networks and compare their results to the optimal solutions obtained using Integer Linear Program. The simulation results demonstrate that the approximation algorithms almost always produce near optimal results in a fraction of the time needed to find the optimal solution.

On shortest single/multiple path computation problems in Fiber-Wireless (FiWi) access networks

Fiber-Wireless (FiWi) networks have received considerable attention in the research community in the last few years as they offer an attractive way of integrating optical and wireless technology. As in every other type of networks, routing plays a major role in FiWi networks. Accordingly, a number of routing algorithms for FiWi networks have been proposed. Most of the routing algorithms attempt to find the “shortest path” from the source to the destination. A recent paper proposed a novel path length metric, where the contribution of a link towards path length computation depends not only on that link but also every other link that constitutes the path from the source to the destination. In this paper we address the problem of computing the shortest path using this path length metric. Moreover, we consider a variation of the metric and also provide an algorithm to compute the shortest path using this variation. As multipath routing provides a number of advantages over single path routing, we consider disjoint path routing with the new path length metric. We show that while the single path computation problem can be solved in polynomial time in both the cases, the disjoint path computation problem is NP-complete. We provide optimal solution for the NP-complete problem using integer linear programming and also provide two approximation algorithms with a performance bound of 4 and 2 respectively. The experimental evaluation of the approximation algorithms produced a near optimal solution in a fraction of a second.

Spatio-temporal Signal Recovery from Political Tweets in Indonesia

Online social network community now provides an enormous volume of data for analyzing human sentiment about people, places, events and political activities. It is becoming increasingly clear that analysis of such data can provide great insights on the social, political and cultural aspects of the participants of these networks. As part of the Minerva project, currently underway at Arizona State University, we have analyzed a large volume of Twitter data to understand radical political activity in the provinces of Indonesia. Based on analysis of radical/counter radical sentiments expressed in tweets by Twitter users, we create a Heat Map of Indonesia which visually demonstrates the degree of radical activities in various provinces of Indonesia. We create the Heat Map of Indonesia by computing (i) the Radicalization Index and (ii) the Location Index of each Twitter user from Indonesia, who has expressed some radical sentiment in her tweets. The conclusions derived from our analysis matches significantly with the analysis of Wahid Institute, a leading political think tank of Indonesia, thus validating our results.

On mobile sensor data collection using data mules

The sensor data collection problem using data mules has been studied fairly extensively in the literature. However, in most of these studies, while the mule is mobile, all sensors are stationary. The objective of most of these studies is to minimize the time needed by the mule to collect data from all the sensors and return to the data collection point from where it embarked on its data collection journey. The problem studied in this paper has two major differences with these earlier studies. First, in this study we assume that both the mule as well as the sensors are mobile. Second, we do not attempt to minimize the data collection time. Instead, we minimize the number of mules that will be needed to collect data from all the sensors, subject to the constraint that the data collection process has to be completed within some pre-specified time. We show that the mule minimization problem is NP-Complete and analyze the problem in two settings. We provide solutions to the problem in both settings by first transforming the problem to a generalized version of the minimum flow problem in a network, and then solving it optimally using Integer Linear Programming. Finally, we evaluate our algorithms through experiments and present our results.

Region based fault-tolerant distributed file storage system design under budget constraint

Two independent lines of research, (i) erasure code based file storage system design, and (ii) fault-tolerant network design for spatially correlated (or region-based) failures, have received considerable attention in the networking research community in recent times. A recently proposed (N,K)-coding based distributed file storage scheme ensures complete reconstruction of a file after network fragmentation due to any single region-based fault. For every region of the network, it stores K distinct file segments in one of the largest connected component that results from the fragmentation of the network due to the failure of a region. This distribution scheme provides an all-region fault-tolerant storage system, in the sense that no matter which region of the network fails, a largest connected component of the fragmented network will still have enough distinct file segments with which to reconstruct the file. However, the storage requirement and the associated cost for such an all-region-fault-tolerant storage system may be quite high. As such, with a limited budget it may not be possible to realize such an all-region fault-tolerant storage system. We consider a budget constrained distributed file system design problem and provide solutions that maximizes the number of regions that can be made fault-tolerant, within the specified budget. We show that the problem is NP-complete, and provide an approximation algorithm for the problem. The performance of the approximation algorithm is evaluated through simulation on two real networks. The simulation results demonstrate that the worst case experimental performance is significantly better than the worst case theoretical bound. Moreover, the approximation algorithm almost always produce near optimal solution in a fraction of time needed to find the optimal solution.

Budget constrained relay node placement problem for maximal “connectedness”

The relay node placement problem in the wireless sensor network have been studied extensively in the last few years. The goal of most of these problems is to place the fewest number of relay nodes in the deployment area so that the network formed by the sensors nodes and the relay nodes is connected. Most of these studies are conducted for the unconstrained budget scenario, in the sense that there is an underlying assumption that no matter however many relay nodes are needed to make the network connected, they can be procured and deployed. However, in a fixed budget scenario, the expenses involved in procuring the minimum number of relay nodes to make the network connected may exceed the budget. Although in this scenario, one has to give up the idea of having a network connecting all the sensor nodes, one would still like to have a network with high level of “connectedness”. In the paper we introduce two metrics for measuring “connectedness” of a disconnected graph and study the problem whose goal is to design a network with maximal “connectedness”, subject to a fixed budget constraint. We show that both versions of the problem are NP-complete and provide heuristics for their solution. We show that the problem is non-trivial even when the number of sensor nodes is as few as three. We evaluate the performance of heuristics through simulation.