Some of the applications in modern data networks are delay sensitive (e.g., video and voice). An end-to-end delay analysis is needed to estimate the required network resources of delay sensitive applications. The schedulers used in the network can impact the resulting delays to the applications. When multiple applications are multiplexed in a switch, a scheduler is used to determine the precedence of the arrivals from different applications. Computing the end-to-end delay and queue sizes in a network of schedulers is difficult and the existing solutions are limited to some special cases (e.g., specific type of traffic). The theory of Network Calculus employs the min-plus algebra to obtain performance bounds. Given an upper bound on the traffic arrival in any time interval and a lower bound on the available service (called the service curve) at a network element, upper bounds on the delay and queue size of the traffic in that network element can be obtained. An equivalent end-to-end service curve of a tandem of queues is the min-plus convolution of the service curves of all nodes along the path. A probabilistic end-to-end delay bound using network service curve scales with O(H logH) in the path length H. This improves the results of the conventional method of adding per-node delay bounds scaling with O(H^3). We have used and advanced Network Calculus for end-to-end delay analysis in a network of schedulers. We formulate a service curve description for a large class of schedulers which we call Delta-schedulers. We show that with this service curve, tight single node delay and backlog bounds can be achieved. In an end-to-end scenario, we formulate a new convolution theoii rem which considerably improves the end-to-end probabilistic delay bounds. We specify our probabilistic end-to-end delay and backlog bounds for exponentially bounded burstniess (EBB) traffic arrivals. We show that the end-to-end delay varies considerably by the type of schedulers along the path. Using these bounds, we also show that a if the number of flows increases, the queues inside a network can be analyzed in isolation and regardless of the network effect.

Wireless sensor networks (WSNs) consist of a large number of sensor nodes, capable of on-board sensing and data processing, that are employed to observe some phenomenon of interest. With their desirable properties of flexible deployment, resistance to harsh environment and lower implementation cost, WSNs envisage a plethora of applications in diverse areas such as industrial process control, battle- field surveillance, health monitoring, and target localization and tracking. Much of the sensing and communication paradigm in WSNs involves ensuring power efficient transmission and finding scalable algorithms that can deliver the desired performance objectives while minimizing overall energy utilization. Since power is primarily consumed in radio transmissions delivering timing information, clock synchronization represents an indispensable requirement to boost network lifetime. This dissertation focuses on deriving efficient estimators and performance bounds for the clock parameters in a classical frequentist inference approach as well as in a Bayesian estimation framework. A unified approach to the maximum likelihood (ML) estimation of clock offset is presented for different network delay distributions. This constitutes an analytical alternative to prior works which rely on a graphical maximization of the likelihood function. In order to capture the imperfections in node oscillators, which may render a time-varying nature to the clock offset, a novel Bayesian approach to the clock offset estimation is proposed by using factor graphs. Message passing using the max-product algorithm yields an exact expression for the Bayesian inference problem. This extends the current literature to cases where the clock offset is not deterministic, but is in fact a random process. A natural extension of pairwise synchronization is to develop algorithms for the more challenging case of network-wide synchronization. Assuming exponentially distributed random delays, a network-wide clock synchronization algorithm is proposed using a factor graph representation of the network. Message passing using the max- product algorithm is adopted to derive the update rules for the proposed iterative procedure. A closed form solution is obtained for each node's belief about its clock offset at each iteration. Identifying the close connections between the problems of node localization and clock synchronization, we also address in this dissertation the problem of joint estimation of an unknown node's location and clock parameters by incorporating the effect of imperfections in node oscillators. In order to alleviate the computational complexity associated with the optimal maximum a-posteriori estimator, two iterative approaches are proposed as simpler alternatives. The first approach utilizes an Expectation-Maximization (EM) based algorithm which iteratively estimates the clock parameters and the location of the unknown node. The EM algorithm is further simplified by a non-linear processing of the data to obtain a closed form solution of the location estimation problem using the least squares (LS) approach. The performance of the estimation algorithms is benchmarked by deriving the Hybrid Cramer-Rao lower bound (HCRB) on the mean square error (MSE) of the estimators. We also derive theoretical lower bounds on the MSE of an estimator in a classical frequentist inference approach as well as in a Bayesian estimation framework when the likelihood function is an arbitrary member of the exponential family. The lower bounds not only serve to compare various estimators in our work, but can also be useful in their own right in parameter estimation theory.

Some of the applications in modern data networks are delay sensitive (e.g., video and voice). An end-to-end delay analysis is needed to estimate the required network resources of delay sensitive applications. The schedulers used in the network can impact the resulting delays to the applications. When multiple applications are multiplexed in a switch, a scheduler is used to determine the precedence of the arrivals from different applications. Computing the end-to-end delay and queue sizes in a network of schedulers is difficult and the existing solutions are limited to some special cases (e.g., specific type of traffic). The theory of Network Calculus employs the min-plus algebra to obtain performance bounds. Given an upper bound on the traffic arrival in any time interval and a lower bound on the available service (called the service curve) at a network element, upper bounds on the delay and queue size of the traffic in that network element can be obtained. An equivalent end-to-end service curve of a tandem of queues is the min-plus convolution of the service curves of all nodes along the path. A probabilistic end-to-end delay bound using network service curve scales with O(H logH) in the path length H. This improves the results of the conventional method of adding per-node delay bounds scaling with O(H^3). We have used and advanced Network Calculus for end-to-end delay analysis in a network of schedulers. We formulate a service curve description for a large class of schedulers which we call Delta-schedulers. We show that with this service curve, tight single node delay and backlog bounds can be achieved. In an end-to-end scenario, we formulate a new convolution theoii rem which considerably improves the end-to-end probabilistic delay bounds. We specify our probabilistic end-to-end delay and backlog bounds for exponentially bounded burstniess (EBB) traffic arrivals. We show that the end-to-end delay varies considerably by the type of schedulers along the path. Using these bounds, we also show that a if the number of flows increases, the queues inside a network can be analyzed in isolation and regardless of the network effect.

Dans ce mémoire, nous nous intéressons à des algorithmes de sélection de modèles dans un contexte de régression linéaire et logistique. Nous expliquons premièrement les notions de régression linéaire et logistique et deux critères de sélection, AIC et BIC. Ensuite, nous faisons une revue des aspects théoriques des algorithmes les plus connus en détaillant deux d'entre eux, Leaps and Bounds et Occam’s Window. Pour ces deux derniers, nous présentons aussi les détails pratiques des logiciels qui font leur implantation. La partie finale est consacrée à l'étude des trois méthodes de sélection des modèles basées sur les algorithmes Leaps and Bounds, Occam’s Window et sur une combinaison entre les deux, en utilisant la technique du moyennage de modèles. Nous présentons les performances de prédiction calculées à l'aide de la technique de validation croisée et les temps d'exécution de ces trois méthodes pour plusieurs jeux de données. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : sélection de modèles, moyennage de modèles, régression linéaire, régression logistique, AIC, BIC, algorithme Leaps and Bounds, algorithme Occam’s Window, validation croisée.

This thesis presents several algorithms that update the vertex separation of a tree after the tree is modified; the vertex separation of a graph measures the largest number of vertices to the left of and including a vertex that are adjacent to vertices to the right of the vertex, when the vertices in the graph are arranged in the best possible linear ordering. Vertex separation was introduced by Lipton and Tarjan and has since been applied mainly in VLSI design. The tree is modified by either attaching another tree or removing a subtree. The first algorithm handles the special case when another tree is attached to the root, and the second algorithm updates the vertex separation after a subtree of the root is removed. The last two algorithms solve the more general problem when subtrees are attached to or removed from arbitrary vertices; they have good running time performance only in the amortized sense. The running time of all our algorithms is sublinear in the number of vertices in the tree, assuming certain information is precomputed for the tree. This improves upon current algorithms by Skodinis and Ellis, Sudborough, and Turner, both of which have linear running time for this problem. Lower and upper bounds on the vertex separation of a general graph are also derived. Furthermore, analogous bounds are presented for the cutwidth of a general graph, where the cutwidth of a graph equals the maximum number of edges that cross over a vertex, when the vertices in the graph are arranged in the best possible linear ordering.

Routing messages between pairs of nodes is one of the most fundamental tasks in any distributed computing system. An Interval Routing Scheme (IRS) is a well-known, space-efficient routing strategy for routing messages in a network. In this scheme, each node of the network is assigned an integer label and each link at each node is labeled with an interval. The interval assigned to a link l at a node v indicates the set of destination addresses of the messages which should be forwarded through l at v. When studying interval routing schemes, there are two main problems to be considered: a) Which classes of networks do support a specific routing scheme? b) Assuming that a given network supports IRS, how good are the paths traversed by messages? The first problem is known as the characterization problem and has been studied for several types of IRS. In this thesis, we study the characterization problem for various schemes in which the labels assigned to the vertices are d-ary integer tuples (d-dimensional IRS) and the label assigned to each link of the network is a list of d 1-dimensional intervals. This is known as Multi-dimensional IRS (MIRS) and is an extension of the the original IRS. We completely characterize the class of network which support MIRS for linear (which has no cyclic intervals) and strict (which has no intervals assigned to a link at a node v containing the label of v) MIRS. In real networks usually the costs of links may vary over time (dynamic cost links). We also give a complete characterization for the class of networks which support a certain type of MIRS which routes all messages on shortest paths in a network with dynamic cost links. The main criterion used to measure the quality of routing (the second problem) is the length of routing paths. In this thesis we also investigate this problem for MIRS and prove two lower bounds on the length of the longest routing path. These are the only known general results for MIRS. Finally, we study the relationship between various types of MIRS and the problem of drawing a hypergraph. Using some of our results we prove a tight bound on the number of dimensions of the space needed to draw a hypergraph.

The main goal of this thesis is to investigate the complexity of a variety of problems related to text indexing and text searching. We present new data structures that can be used as building blocks for full-text indices which occupies minute space (FM-indexes) and wavelet trees. These data structures also can be used to represent labeled trees and posting lists. Labeled trees are applied in XML documents, and posting lists in search engines. The main emphasis of this thesis is on lower bounds for time-space tradeoffs for the following problems: the rank/select problem, the problem of representing a string of balanced parentheses, the text retrieval problem, the problem of computing a permutation and its inverse, and the problem of representing a binary relation. These results are divided in two groups: lower bounds in the cell probe model and lower bounds in the indexing model. The cell probe model is the most natural and widely accepted framework for studying data structures. In this model, we are concerned with the total space used by a data structure and the total number of accesses (probes) it performs to memory, while computation is free of charge. The indexing model imposes an additional restriction on the storage: the object in question must be stored in its raw form together with a small index that facilitates an efficient implementation of a given set of queries, e.g. finding rank, select, matching parenthesis, or an occurrence of a given pattern in a given text (for the text retrieval problem). We propose a new technique for proving lower bounds in the indexing model and use it to obtain lower bounds for the rank/select problem and the balanced parentheses problem. We also improve the existing techniques of Demaine and Lopez-Ortiz using compression and present stronger lower bounds for the text retrieval problem in the indexing model. The most important result of this thesis is a new technique for cell probe lower bounds. We demonstrate its strength by proving new lower bounds for the problem of representing permutations, the text retrieval problem, and the problem of representing binary relations. (Previously, there were no non-trivial results known for these problems.) In addition, we note that the lower bounds for the permutations problem and the binary relations problem are tight for a wide range of parameters, e.g. the running time of queries, the size and density of the relation.

In this thesis, we study different Internet pricing schemes and how they can be applied to a multiple ISP environment. We first take a look at the current Internet architecture. Then the different classes that make up the Internet hierarchy are discussed. We also take a look at peering among Internet Service Providers (ISPs) and when it is a good idea for an ISP to consider peering. Moreover, advantages and disadvantages of peering are discussed along with speculations of the evolution of the Internet peering ecosystem. We then consider different pricing schemes that have been proposed and study the factors that make up a good pricing plan. Finally, we apply some game theoretical concepts to discuss how different ISPs could interact together. We choose a pricing model based on a Stackelberg game that takes into consideration the effect of the traffic variation among different customers in a multiple ISP environment. It allows customers to specify their desired QoS in terms of maximum allowable end-to-end delay. Customers only pay for the portion of traffic that meet this delay bound. Moreover, we show the effectiveness of adopting this model through a comparison with a model that does not take traffic variation into account. We also develop a naïve case and compare it to our more sophisticated approach.

Moment Problems with Applications to Value-At-Risk and Portfolio Management By Ruilin Tian May 2008 Committee Chair: Dr. Samuel H. Cox Major Department: Risk Management and Insurance My dissertation provides new applications of moment theory and optimization to financial and insurance risk management. In the investment and managerial areas, one often needs to determine some measure of risk, especially the risk of extreme events. However, complete information of the underlying outcomes is usually unavailable; instead one has access to partial information such as the mean, variance, mode, or range. In Chapters 2 and 3, we find the semiparametric upper and lower bounds for the value-at-risk (VaR) with incomplete information, that is, moments of the underlying distribution. When a single variable is concerned, bounds on VaR are computed to obtain a 100% confidence interval. When the sample financial data have a global maximum, we show that unimodal assumption tightens the optimal bounds. Next we further analyze a function of two correlated random variables. Specifically, we find bounds on the probability of two joint extreme events. When three or more variables are involved, the multivariate problem can sometimes be converted to a single variable problem. In all cases, we use the physical measure rather than the commonly used equivalent pricing probability measure. In addition to solving these problems using the traditional approach based on the geometry of a moment problem, a more efficient method is proposed to solve a general class of moment bounds via semidefinite programming. In the last part of the thesis, we apply optimization techniques to improve financial portfolio risk management. Instead of considering VaR, we work with a coherent risk measure, the conditional VaR (CVaR). As an extension of Krokhmal et al. (2002), we impose CVaR-related functions to the portfolio selection problem. The CVaR approach sets a β-level CVaR as the objective function and maximizes the worst case on the tail of the distribution. The CVaR-like constraints approach adds a set of CVaR-like constraints to the traditional Markowitz problem, reshaping the portfolio distribution. Both methods greatly increase the skewness of portfolios, although the CVaR approach may lose control of the variance. This capability of increasing skewness is very attractive to the investors who may prefer higher probability of obtaining higher returns. We compare the CVaR-related approaches to some other popular portfolio optimization methods. Our numerical analysis provides empirical support for the superiority of the CVaR-like constraints approach in terms of portfolio efficiency.

This thesis presents several algorithms that update the vertex separation of a tree after the tree is modified; the vertex separation of a graph measures the largest number of vertices to the left of and including a vertex that are adjacent to vertices to the right of the vertex, when the vertices in the graph are arranged in the best possible linear ordering. Vertex separation was introduced by Lipton and Tarjan and has since been applied mainly in VLSI design. The tree is modified by either attaching another tree or removing a subtree. The first algorithm handles the special case when another tree is attached to the root, and the second algorithm updates the vertex separation after a subtree of the root is removed. The last two algorithms solve the more general problem when subtrees are attached to or removed from arbitrary vertices; they have good running time performance only in the amortized sense. The running time of all our algorithms is sublinear in the number of vertices in the tree, assuming certain information is precomputed for the tree. This improves upon current algorithms by Skodinis and Ellis, Sudborough, and Turner, both of which have linear running time for this problem. Lower and upper bounds on the vertex separation of a general graph are also derived. Furthermore, analogous bounds are presented for the cutwidth of a general graph, where the cutwidth of a graph equals the maximum number of edges that cross over a vertex, when the vertices in the graph are arranged in the best possible linear ordering.