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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.

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We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyper-strips (resp. hyper-cylinders) so that the maximum width of a hyper-strip (resp., the maximum diameter of a hyper-cylinder) is minimized. Let w be the smallest value so that S can be covered by k hyper-strips (resp. hyper-cylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NP-Hard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...

We present improved combinatorial approximation algorithms for the uncapacitated facility location and k-median problems. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of 2:414 + in ~ O(n 2 =) time. This also yields a bicriteria approximation tradeoff of (1 +; 1+ 2=) for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible. Combining greedy improvement and cost scaling with a recent primal dual algorithm for facility location due to Jain and Vazirani, we get an approximation ratio of 1.853 in ~ O(n 3 ) time. This is already very close to the approximation guarantee of the best known algorithm which is LP-based. Further, combined with the best known LP-based algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving 1.728....

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Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application, and which should also be useful in other applications. The goal is to efficiently maintain clusters of small diameter as new points are inserted. We analyze several natural greedy algorithms and demonstrate that they perform poorly. We propose new deterministic and randomized incremental clustering algorithms which have a provably good performance. We complement our positive results with lower bounds on the performance of incremental algorithms. Finally, we consider the dual clustering problem where the clusters are of fixed diameter, and the goal is to minimize the number of clusters. 1 Introduction We consider the following problem: as a sequence of points from a metric...

We present a simple and natural greedy algorithm for the metric uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73. Furthermore, we will show that our algorithm has a property which allows us to apply the technique of Lagrangian relaxation. Using this property, we can nd better approximation algorithms for many variants of the facility location problem, such as the capacitated facility location problem with soft capacities and a common generalization of the k-median and facility location problem. We will also prove a lower bound on the approximability of the k-median problem.

We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.

Beacon placement strongly affects the quality of spatial localization, a critical service for context-aware applications in wireless sensor networks; yet this aspect of localization has received little attention. Fixed beacon placement approaches such as uniform and very dense placement are not always viable and will be inadequate in very noisy environments in which sensor networks may be expected to operate (with high terrain and propagation uncertainties). In this paper, we motivate the need for empirically adaptive beacon placement and outline a general approach based on exploration and instrumentation of the terrain conditions by a mobile human or robot agent. We design, evaluate and analyze three novel adaptive beacon placement algorithms using this approach for localization based on RF-proximity. In our evaluation, we find that beacon density rather than noise level has a more significant impact on beacon placement algorithms. Our beacon placement algorithms are applicable to a low (beacon) density regime of operation. Noise makes moderate density regimes more improvable.