Sujogya Banerjee

Region-based connectivity - a new paradigm for design of fault-tolerant networks

The studies in fault-tolerance in networks mostly focus on the connectivity of the graph as the metric of faulttolerance. If the underlying graph is k-connected, it can tolerate up to k — 1 failures. In measuring the fault tolerance in terms of connectivity, no assumption regarding the locations of the faulty nodes are made - the failed nodes may be close to each other or far from each other. In other words, the connectivity metric has no way of capturing the notion of locality of faults. However in many networks, faults may be highly localized. This is particularly true in military networks, where an enemy bomb may inflict massive but localized damage to the network. To capture the notion of locality of faults in a network, a new metric region-based connectivity (RBC) was introduced in [1]. It was shown that RBC can achieve the same level of fault-tolerance as the metric connectivity, with much lower networking resources. The study in [1] was restricted to single region fault model (SRFM), where faults are confined to one region only. In this paper, we extend the notion of RBC to multiple region fault model (MRFM), where faults are no longer confined to a single region. As faults in MRFM are still confined to regions, albeit multiple of them, it is different from unconstrained fault model where no constraint on locality of faults is imposed. The MRFM leads to several new concepts, such as region-disjoint paths and region cuts. We show that the classical result, the maximum number of node-disjoint paths between a pair of nodes is equal to the minimum number of nodes whose removal disconnects the pair, is no longer valid when region-disjoint paths and region cuts are considered. We prove that the problems of finding (i) the maximum number of region-disjoint paths between a pair of nodes, and (ii) minimum number of regions whose removal disconnect a pair of nodes, are both NP-complete. We provide heuristic solution to these two problems and evaluate their efficacy by comparing the results with optimal solutions.

Design and Analysis of Networks with Large Components in Presence of Region-Based Faults

Connectivity k(G) of a network G is traditionally considered to be the primary metric for evaluation of its fault tolerance capability. However, connectivity as a metric has several limitations - e.g., it has no mechanism to distinguish between localized and random faults. Also it does not provide any information about the network state, if number of failures exceed k(G). The network state information that might be of interest in such a scenario is the size of the largest connected component. In this paper, we address both these limitations and introduce a new metric called region-based largest component size (RBLCS), that provides the largest size of the component in which the network decomposes once all the nodes of a region fail. We study the computational complexity of finding RBLCS for a given network. In addition, we study the problem of least cost design of a network with a target value of RBLCS. We prove that the optimal design problem is NP-complete and present a heuristic to solve the problem. We evaluate our heuristic by comparing its solutions with the optimal solutions. Experimental results demonstrate that our heuristic produces near optimal solution in a fraction of time needed to find the optimal.

Beyond connectivity - new metrics to evaluate robustness of networks

Robustness or fault-tolerance capability of a network is an important design parameter in both wired and wireless networks. Connectivity of a network is traditionally considered to be the primary metric for evaluation of its fault-tolerance capability. However, connectivity κ(G) (for random faults) or region-based connectivity κR(G) (for spatially correlated or region-based faults, where the faults are confined to a region R) of a network G, does not provide any information about the network state, (i.e., whether the network is connected or not) once the number of faults exceeds κ(G) or κR(G). If the number of faults exceeds κ(G) or κR(G), one would like to know, (i) the number of connected components into which G decomposes, (ii) the size of the largest connected component, (iii) the size of the smallest connected component. In this paper, we introduce a set of new metrics that computes these values. We focus on one particular metric called region-based component decomposition number (RBCDN), that measures the number of connected components in which the network decomposes once all the nodes of a region fail. We study the computational complexity of finding RBCDN of a network. In addition, we study the problem of least cost design of a network with a target value of RBCDN. We show that the optimal design problem is NP-complete and present an approximation algorithm with a performance bound of O(log K + 4log n), where n denotes the number of nodes in the graph and K denotes a target value of RBCDN. We evaluate the performance of our algorithm by comparing it with the performance of the optimal solution. Experimental results demonstrate that our algorithm produces near optimal solution in a fraction of time needed to find an optimal solution.

Dynamic Lightpath Allocation in Translucent WDM Optical Networks

The optical reach (the distance an optical signal can travel before the signal quality degrades to a level that necessitates regeneration) ranges from 500 to 2000 miles. To establish a lightpath of length greater than the optical reach, it is necessary to regenerate optical signals. In a translucent optical network, there are regeneration points, where the signal undergoes Optical-Electronic-Optical (O-E-O) conversion. In this paper we have proposed routing algorithms for translucent networks in a dynamic lightpath allocation environment in which requests for communication arrive continuously. In response to each request for communication, the objective is to establish, if possible, a path, from the source to the destination of the request for communication, so that a lightpath may be established, using the path that requires the fewest stages of regeneration. In practical transparent networks, a lightpath must satisfy the wavelength continuity constraint. However, in a translucent network, this constraint can be relaxed at the regeneration points. We have proposed an Integer Linear Program, to give the optimum results for small networks, as well as an efficient heuristic for this problem that works for larger networks. We have evaluated the heuristic through extensive simulations to establish that the heuristic produces close-to-optimal solutions in a fraction of the time needed for the optimal solutions. Our extensive evaluations demonstrate the relative impact of a set of network resources, such as (i) the number of regenerators, (ii) the optical reach of the regenerators and (iii) the number of wavelengths, on the network performance, measured in terms of the call blocking probability. To the best of our knowledge this is the first study that undertakes such an evaluation for translucent networks.

On region-based fault tolerant design of distributed file storage in networks

Distributed storage of data files in different nodes of a network enhances the reliability of the data by offering protection against node failure. In the (N,K),N ≥ K file distribution scheme, from a file F of size |F|, N segments of size |F|/K are created in such a way that it is possible to reconstruct the entire file, just by accessing any K 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 case of node 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 goal of this research is to devise a file segment distribution scheme so that, even if the network becomes disconnected due to any region fault, at least one of the largest connected components will have at least K distinct file segments with which to reconstruct the entire file. The distribution scheme will also ensure that the total storage requirement is minimized. We provide an optimal solution through Integer Linear Programming and an approximation solution with a guaranteed performance bound of O(ln n) to solve the problem for any arbitrary network. The performance of the approximation algorithm is evaluated by simulation on two real networks.

A System for Ranking Organizations Using Social Scale Analysis

In this paper we utilize feature extraction and model fitting techniques to process the rhetoric found in the web sites of 23 Indonesian religious organizations -- comprising a total of 37,000 articles dating from 2005 to 2011 -- to profile their ideology and activity patterns along a hypothesized radical/counter-radical scale. We rank these organizations by assigning them to probable positions on the scale. We show that the developed Rasch model fits the data using Andersens LR-test. We create a gold standard of the ranking of these organizations through an expertise elicitation tool. We compute expert-to-expert agreements, and we present experimental results comparing the performance of three different baseline methods to show that the Rasch model not only outperforms our baseline methods, but it is also the only system that performs at expert-level accuracy.

Impact of region-based faults on the connectivity of wireless networks

The traditional studies on fault-tolerance in networks assume that the faults are random in nature, i.e., the probability of a node failing is independent of its location in the deployment area. However, this assumption is no longer valid if the faults are spatially correlated. In this paper we focus on the study of the impact of region-based faults on wireless networks. Most of the studies on connectivity of wireless networks assume a unit disk graph model, i.e., links exist between two nodes if they are within a circular transmission range of one another. However, the unit disk graph model does not capture wireless communication environment accurately. The log-normal shadow fading model for communication was introduced to overcome the limitations of the unit disk graph model. In this paper we investigate connectivity issues of wireless networks in a log-normal shadow fading environment where the faults are spatially correlated. If d_min(G) denotes the minimum node degree of the network, we provide the analytical expression and method for computing P(d_min(G) >= 1) in a region-based fault scenario, where P(d_min(G) >= 1) denotes the probability of the minimum node degree being at least 1. Through extensive simulation, we find P(kG) >= 1), where k(G) represents the connectivity of the graph G formed by the distribution of nodes on a 2D plane and examine the relationship between P(d_min(G) >= 1) and P(k(G) >= 1).

Perspective Analysis for Online Debates

Internet and social media devices created a new public space for online debate on political and social topics. A debate is defined as a formal discussion on a set of related topics in a public meeting, in which opposing perspectives and arguments are put forward. In this paper, we develop automated perspective discovery techniques which would contribute to the understanding of features (i.e. social, political, cultural, religious beliefs, goals, and practices) shared by each side of the debate. Secondly, we show that, compared to a semi-automated process, our perspective discovery algorithms not only identify larger number of relevant features, but they also yield a higher accuracy scaling of moderate to extreme organizations on both sides of a debate.

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.

A system for ranking organizations using social scale analysis

In this paper, we utilize feature extraction and model-fitting techniques to process the rhetoric found in the web sites of 23 Indonesian Islamic religious organizations to profile their ideology and activity patterns along a hypothesized radical/counter-radical scale, and present an end-to-end system that is able to help researchers to visualize the data in an interactive fashion on a timeline. The subject data of this study is 37,000 articles downloaded from the web sites of these organizations dating from 2001 to 2011. We develop algorithms to rank these organizations by assigning them to probable positions on the scale. We show that the developed Rasch model fits the data using Andersen’s LR-test. We create a gold standard of the ranking of these organizations through an expertise elicitation tool. We compute expert-to-expert agreements, and we present experimental results comparing the performance of three baseline methods to show that the Rasch model not only outperforms the baseline methods, but it is also the only system that performs at expert-level accuracy.