Abstract—Recently there has been an increasing deployment of content distribution networks (CDNs) that offer hosting services to Web content providers. CDNs deploy a set of servers distributed throughout the Internet and replicate provider content across these servers for better performance and availability than centralized provider servers. Existing work on CDNs has primarily focused on techniques for efficiently redirecting user requests to appropriate CDN servers to reduce request latency and balance load. However, little attention has been given to the development of placement strategies for Web server replicas to further improve CDN performance. In this paper, we explore the problem of Web server replica placement in detail. We develop several placement algorithms that use workload information, such as client latency and request rates, to make informed placement decisions. We then evaluate the placement algorithms using both synthetic and real network topologies, as well as Web server traces, and show that the placement of Web replicas is crucial to CDN performance. We also address a number of practical issues when using these algorithms, such as their sensitivity to imperfect knowledge about client workload and network topology, the stability of the input data, and methods for obtaining the input. Keywords—World Wide Web, replication, replica placement algorithm, content distribution network (CDN). I.

We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchand-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. Wethen discuss computational issues and implementation of column generation, branch-andbound algorithms, including special branching rules and e cient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality. 1

This report describes an implementation of the Lin-Kernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 7397-city problem (the largest nontrivial problem instance solved to optimality today). Furthermore, the algorithm has improved the best known solutions for a series of large-scale problems with unknown optima, among these an 85900-city problem. 1.

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We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of two extensions that are very relevant to practical problems: the case of multiple cuts and the case of deep cuts. We further examine extensions to problems including feasible sets partially described by an explicit barrier function, and to the case of nonlinear cuts. Finally, we review several implementation issues and discuss some applications.

This paper is concerned with the longstanding problem of optimal unit commitment in an electric power system. We follow the traditional formulation of this problem which gives rise to a large-scale, dynamic, mixed-integer programming problem. We describe a solution methodology based on duality, Lagrangian relaxation and nondifferentiable optimization that has two unique features. First, computational requirements typically grow only linearly witb the number of generating units. Second, the duality gap decreases in relative terms as the number of units increases, and as a result our algorithm tends to actually perform better for problems of large size. This allows for the first time consistently reliable solution of large practical problems involving several hundreds of units within realistic time constraints. Aside from the unit commilment problem. this methodology is applicable to a broad class of large-scale dpamic scheduling and resource allocation problems involving integer variables.

Virtual Path (VP) concept has been gaining attention in terms of effective deployment of ATM (Asynchronous Transfer Mode) networks in recent years. In a recent paper, we have outlined a framework and models for network design and management of dynamically reconfigurable ATM networks based on the virtual path concept from a network planning and management perspective. Our approach has been based on statistical multiplexing of traffic within a traffic class by using a virtual path for the class and deterministic multiplexing of different virtual paths, and on providing dynamic bandwidth and reconfigurability through virtual path concept depending on traffic load during the course of the day. In this paper, we discuss in detail a multi-hour, multi-traffic class network (capacity) design model for providing specified quality-of-service in such dynamically reconfigurable networks; this is done based on the observation that statistical multiplexing of virtual circuits for a traffic class in ...

Scheduling is one of the most basic but the most difficult problems encountered in the manufacturing industry. Generally, some degree of time-consuming and impractical enumeration is required to obtain optimal solutions. Industry has thus relied on a combination of heuristics and simulation to solve the problem, resulting in unreliable and often infeasible schedules. Yet, there is a great need for an improvement in scheduling operations in complex and turbulent manufacturing environments. The logical strategy is to find scheduling methods which consistently generate good schedules efficiently. However, it is often difficult to measure the quality of a schedule without knowing the optimum. In this paper, the practical scheduling of three manufacturing environments are examined in the increasing order of complexity. The first problem considers scheduling singleoperation jobs on parallel, identical machines; the second one is concerned with scheduling multiple-operation jobs with simple ...

In this paper, we consider solution approaches to a multi-hour combined capacity design and routing problem which arises in the design of dynamically reconfigurable broadband communication networks that uses the virtual path concept. We present a comparative evaluation of four approaches, namely: a genetic algorithm; a Lagrangean relaxation based subgradient optimization method; a generalized proximal point algorithm with subgradient optimization; and finally, a hybrid approach where the subgradient based method is combined with a genetic algorithm. Our computational experience on a set of test problems of varying network sizes shows that the hybrid approach often is the desirable choice in obtaining the minimum cost network while the genetic algorithm based approach has the most difficulty in solving large scale problems. Keywords: Broadband network design, multi-hour network routing and capacity design, combinatorial optimization, genetic algorithm, duality and subgradient optimizati...

The Quadratic Knapsack Problem (QKP) calls for maximizing a quadratic objective function subject to a knapsack constraint, where all coefficients are assumed to be nonnegative and all variables are binary. The problem has applications in location and hydrology, and generalizes the problem of checking whether a graph contains a clique of a given size. We propose an exact branch-and-bound algorithm for QKP, where upper bounds are computed by considering a Lagrangian relaxation which is solvable through a number of (continuous) knapsack problems. Suboptimal Lagrangian multipliers are derived by using subgradient optimization and provide a convenient reformulation of the problem. We also discuss the relationship between our relaxation and other relaxations presented in the literature. Heuristics, reductions and branching schemes are finally described. In particular, the processing of each node of the branching tree is quite fast: We do not update the Lagrangian multipliers, and use suitabl...