Uttam K. Sarkar

Modeling full-length video using Markov-modulated gamma-based framework

All traffic models for MPEG-like encoded variable bit rate (VBR) video can be broadly categorized into 1) data-rate models (DRMs) and 2) frame-size models (FSMs). Almost all proposed VBR traffic models are DRMs. DRMs generate only data arrival rate, and are good for estimating average packet-loss and ATM buffer overflowing probabilities, but fail to identify such details as percentage of frames affected. FSMs generate sizes of individual MPEG frames, and are good for studying frame loss rate in addition to data loss rate. Among three previously proposed FSMs: 1) one generates frame sizes for full-length movies without preserving group-of-pictures (GOP) periodicity; 2) one generates VBR video traffic for news videos from scene content description provided to it; and 3) one generates frame sizes for full-length movies without preserving size-based video-segment transitions. In this paper, we propose two FSMs that generate frame sizes for full-length VBR videos preserving both GOP periodicity and size-based video-segment transitions.First, two-pass algorithms for analysis of full-length VBR videos are presented. After two-pass analysis, these algorithms identify size-based classes of video shots into which the GOPs are partitioned. Frames in each class produce three data sets, one each for I-, B-, and P-type frames. Each of these data sets is modeled with an axis-shifted Gamma distribution. Markov renewal processes model (size-based) video segment transitions. We have used QQ plots to show visual similarity of model-generated VBR video data sets with original data set. Leaky-bucket simulation study has been used to show similarity of data and frame loss rates between model-generated VBR videos and original video. Our study of frame-based VBR video revealed that even a low data-loss rate could affect a large fraction of I frames, causing a significant degradation of the quality of transmitted video.

Reducing reexpansions in iterative-deepening search by controlling cutoff bounds

Abstract It is known that a best-first search algorithm like A∗ [5, 6] requires too much space (which often renders it unusable) and a depth-first search strategy does not guarantee an optimal cost solution. The iterative-deepening algorithm IDA∗ [4] achieves both space and cost optimality for a class of tree searching problems. However, for many other problems, it takes too much of computation time due to excessive reexpansion of nodes. This paper presents a modification of IDA∗ to an admissible iterative depth-first branch and bound algorithm IDA∗_CR for trees which overcomes this drawback of IDA∗ and operates much faster using the same amount of storage. Algorithm IDA∗_CRA, a bounded suboptimal cost variation of IDA∗_CR is also presented in order to reduce the execution time still further. Results with the 0/1 Knapsack Problem, Traveling Salesman Problem, and the Flow Shop Scheduling Problem are shown.

Improving greedy algorithms by lookahead-search

Abstract This paper shows that repeated application of a greedy approximation algorithm on some suitably selected subproblems of a problem often leads to a solution which is better than the solution produced by the greedy algorithm applied to the original problem. The lookahead search technique, a polynomial time algorithm introduced here, describes how a greedy algorithm can be utilized in a search process in order to improve the quality of the solution. For the 0/1 knapsack problem and the problem of scheduling independent tasks the lookahead technique is shown to guarantee ϵ-bounded solutions. For the problem of scheduling independent tasks, it has been established that even the simplified version of the lookahead technique provides a bound which is strictly better than the greedy algorithm used in lookahead search. Experimental results are shown for 0/1 knapsack problem, bin packing, Euclidean TSP, and the problem of scheduling independent tasks.

Identifying influential stock indices from global stock markets: A social network analysis approach

Abstract We have proposed a method to rank the stock indices from across the globe using social network analysis approach. The temporal evolution of correlation network and Minimum Spanning Tree (MST) of global stock indices have been analyzed using weekly returns of 93 stock indices for five-year period from the year 2006 through 2010 obtained from Bloomberg. We have chosen this period to study the behaviour of the stock market network before and after the collapse of Lehman Brothers in the USA. Our study attempts to answer the questions about identifying the most influential stock indices in the global stock market, regional influence on the comovement of stock indices, and the impact of the collapse of Lehman Brothers in the USA and the associated global financial crisis that followed on the dynamics of stock market network.

Study of long-duration MPEG-trace segmentation methods for developing frame-size-based traffic models

Texture and temporal variations in scenes, and peculiarities of MPEG compression algorithms result in very complex frame-size data sets for any long-duration variable bit rate (VBR) video. A major hurdle in capturing the statistical behavior of such a data trace can be removed by segmentation of all frames into an appropriate number of analytically characterizable classes. However, video-trace segmentation techniques, particularly those which also enable preserving periodicity of group of pictures (GOP) in the modeled data, are lacking in the literature.In this paper, we propose and evaluate few techniques for segmenting frame-size data sets in any long-duration video trace. The proposed techniques partition the group of pictures in a video into size-based groups called shot-classes. Frames in each shot-class have three data-sets--one each for intra (I-), bi-directional (B-), and predictive (P-) type frames. We have evaluated the performance of the proposed segmentation techniques by modeling each of I-, B-, and P-type frame in each shot-class by a Gamma distribution. Accuracy and usefulness of the proposed segmentation methods in building frame-size traffic models have been evaluated by QQ plots and the leaky-bucket simulation study. The results reveal that one of the segmentation techniques is very effective in characterizing the frame-size data behavior in a long-duration VBR video.

Segmenting full-length VBR video into shots for modeling with Markov-modulated gamma-based framework

All traffic models for MPEG-like encoded variable bit rate (VBR) video can be categorized into (i) data rate models (DRMs), and (ii) frame size models (FSMs). Almost all proposed VBR traffic models are DRMs. Since DRMs generate only data arrival rate, they are good for estimating average packet-loss and ATM buffer over-flowing probabilities, but fail to identify such details as percentage of frames affected. FSMs generate sizes of individual MPEG frames, and are good for studying frame loss rate in addition to data loss rate. Among three previously proposed FSMs: (i) one generates frame sizes for full-length movies without preserving GOP-periodicity; (ii) another generates frame sizes for full-length movies without preserving size-based video-segment transitions; and (iii) the third generates VBR video traffic for news videos from scene content description provided to it presupposing a proper segmentation. In this paper, we propose two segmentation techniques for VBR videos - (a) Equal Number of GOPs in all shot classes (ENG), and (b) Geometrically Increasing Interval Lengths for shot classes (GIIL). Each technique partitions the GOPs in the video into size-based shot classes. Frames in each class produce three data-sets one each for I-, B-, and P-type frames. Each of these data-sets can be modeled with an axis shifted Gamma distribution. Markov renewal processes model interclass transitions. We have used QQ plots to show visual similarity of model-generated VBR video data-sets with original data-set. Leaky-bucket simulation study has been used to show similarity of data and frame loss rates between model-generated videos and original video. Our study of frame-based VBR video revealed GIIL segmentation technique separates the I-, B-, and P- frames in well behaved shot classes whose statistical properties can be captured by Gamma-based models.

A Social Network Approach to Examine the Role of Influential Stocks in Shaping Interdependence Structure in Global Stock Markets

This paper investigates the role of influential stocks in shaping the emergent system-level interdependence in global stock markets using a large set of stocks selected from major stock market indices from across the globe. We have proposed a method to identify influential stocks using various centrality measures used in social network analysis literature. Our study shows how these influential stocks provide key linkages in integrating the global stock markets as an interconnected system. We have also shown that the regional influence dominates over the economic sector influence in shaping the topological structure of stock market network. The study also captures the change in the topology of this network following the collapse of Lehman Brothers.

A simple 0.5-bounded greedy algorithm for the 0/1 knapsack problem

The Non-Increasing First Fit (NIFF) greedy algorithm for the 0/1 knapsack problem does not provide a bounded solution. In this paper a simple modification of this greedy procedure is proposed whose solution is no worse than the solution found by the NIFF algorithm and is guaranteed to be 0.5-bounded. A further modification of the proposed algorithm is shown to improve the bound to 1/3 for the special case of the problem when profit per unit weight is the same for all objects. The bounds obtained are shown to be tight. Experiments were performed with random instances of the problem in order to compare the quality of the solution of this algorithm and that of the NIFF algorithm relative to the optimal solution.

A social network approach to change detection in the interdependence structure of global stock markets

A novel method is proposed to rank the stock indices from across the globe to capture changes in the dominance of an index with respect to other indices. A correlation-based network structure is formulated and centrality measures are used to track these changes. Temporal evolution of the minimum spanning tree derived from the network of 93 stock indices worldwide has been analyzed with data from Bloomberg for the 5-year period from year 2006 through 2010. Measures are suggested for identifying dominant stock indices in the global stock market. It is investigated how the stock market turbulence can be detected by measuring the relative change in the ranks of the stock indices and in the network centralization of the emergent network structure. The study reveals how inclusion of abstract non-living entities such as stock indices in the social network analysis framework can capture the latent interdependence as manifested in the stock market. The chosen period of study encompassed the behavioral change in the stock market network before and after the collapse of Lehman Brothers in the USA, revealing interesting counter-intuitive findings that the turbulence following the collapse of Lehman Brothers had a structure-loosening impact on the global stock market.

Bandwidth estimation for multiplexed videos using MMG-based single video traffic model

A video on demand (VoD) system is expected to transmit many movies over a single channel as demanded by the end users. When several videos are transmitted simultaneously over a link the effective bandwidth required per video is usually much lower than that needed by a single video because of multiplexing gain. Fast and accurate estimation of multiplexing gain is necessary for developing call admission control (CAC) algorithms. Known models which estimate queue size and effective bandwidth of multiplexed video system cannot capture frame size variations in different segments of a video, and are not very useful particularly when the number of videos is not too large. The multinomial model proposed in this paper is built on a Markov-modulated gamma (MMG)-based traffic model of a single video. It takes into consideration average frame size variations in different segments of a video and can predict multiplexing gain for any number of multiplexed videos. The model has been validated using MPEG traces of commercial movies.