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270
On Approximating Arbitrary Metrics by Tree Metrics
 In Proceedings of the 30th Annual ACM Symposium on Theory of Computing
, 1998
"... This paper is concerned with probabilistic approximation of metric spaces. In previous work we introduced the method of ecient approximation of metrics by more simple families of metrics in a probabilistic fashion. In particular we study probabilistic approximations of arbitrary metric spaces by \hi ..."
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Cited by 287 (16 self)
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This paper is concerned with probabilistic approximation of metric spaces. In previous work we introduced the method of ecient approximation of metrics by more simple families of metrics in a probabilistic fashion. In particular we study probabilistic approximations of arbitrary metric spaces by \hierarchically wellseparated tree" metric spaces. This has proved as a useful technique for simplifying the solutions to various problems.
A constantfactor approximation algorithm for the kmedian problem
 In Proceedings of the 31st Annual ACM Symposium on Theory of Computing
, 1999
"... We present the first constantfactor approximation algorithm for the metric kmedian problem. The kmedian problem is one of the most wellstudied clustering problems, i.e., those problems in which the aim is to partition a given set of points into clusters so that the points within a cluster are re ..."
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Cited by 253 (12 self)
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We present the first constantfactor approximation algorithm for the metric kmedian problem. The kmedian problem is one of the most wellstudied clustering problems, i.e., those problems in which the aim is to partition a given set of points into clusters so that the points within a cluster are relatively close with respect to some measure. For the metric kmedian problem, we are given n points in a metric space. We select k of these to be cluster centers, and then assign each point to its closest selected center. If point j is assigned to a center i, the cost incurred is proportional to the distance between i and j. The goal is to select the k centers that minimize the sum of the assignment costs. We give a 6 2 3approximation algorithm for this problem. This improves upon the best previously known result of O(log k log log k), which was obtained by refining and derandomizing a randomized O(log n log log n)approximation algorithm of Bartal. 1
Improved Combinatorial Algorithms for the Facility Location and kMedian Problems
 In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science
, 1999
"... We present improved combinatorial approximation algorithms for the uncapacitated facility location and kmedian 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 ..."
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Cited by 227 (11 self)
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We present improved combinatorial approximation algorithms for the uncapacitated facility location and kmedian 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 LPbased. Further, combined with the best known LPbased algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving 1.728....
Incremental Clustering and Dynamic Information Retrieval
, 1997
"... 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 retri ..."
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Cited by 188 (4 self)
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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.
Variable neighborhood search: Principles and applications
, 2001
"... Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using an ..."
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Cited by 180 (17 self)
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Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a twolevel VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear
The Cache Location Problem
 IEEE/ACM Transactions on Networking
"... This paper studies the problem of where to place network caches. Emphasis is given to caches that are transparent to the clients since they are easier to manage and they require no cooperation from the clients. Our goal is to minimize the overall flow or the average delay by placing a given number o ..."
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Cited by 159 (6 self)
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This paper studies the problem of where to place network caches. Emphasis is given to caches that are transparent to the clients since they are easier to manage and they require no cooperation from the clients. Our goal is to minimize the overall flow or the average delay by placing a given number of caches in the network.
Clustering data streams: Theory and practice
 IEEE TKDE
, 2003
"... Abstract—The data stream model has recently attracted attention for its applicability to numerous types of data, including telephone records, Web documents, and clickstreams. For analysis of such data, the ability to process the data in a single pass, or a small number of passes, while using little ..."
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Cited by 154 (4 self)
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Abstract—The data stream model has recently attracted attention for its applicability to numerous types of data, including telephone records, Web documents, and clickstreams. For analysis of such data, the ability to process the data in a single pass, or a small number of passes, while using little memory, is crucial. We describe such a streaming algorithm that effectively clusters large data streams. We also provide empirical evidence of the algorithm’s performance on synthetic and real data streams. Index Terms—Clustering, data streams, approximation algorithms. 1
ON THE COMPLEXITY OF SOME COMMON GEOMETRIC LOCATION PROBLEMS
 SIAM J. COMPUTING
, 1984
"... Given n demand points in the plane, the pcenter problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo & point to its respective nearest supply point. The pmedian problem is to minimize the sum of distances from demand points to their resp ..."
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Cited by 141 (1 self)
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Given n demand points in the plane, the pcenter problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demo & point to its respective nearest supply point. The pmedian problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the pcenter and the pmedia problems relative to both the Euclidean and the rectilinear metrics are NPhard. In fact, we prove that it is NPhard even to approximate the pcenter problems sufficiently closely. The reductions are from 3satisfiability.
Better Streaming Algorithms for Clustering Problems
 In Proc. of 35th ACM Symposium on Theory of Computing (STOC
, 2003
"... We study cluster ng pr blems in the str aming model, wher e the goal is to cluster a set of points by making one pass (or a few passes) over the data using a small amount of storSD space.Our mainr esult is a r ndomized algor ithm for kMedian prE lem which p duces a constant factor a ..."
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Cited by 91 (1 self)
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We study cluster ng pr blems in the str aming model, wher e the goal is to cluster a set of points by making one pass (or a few passes) over the data using a small amount of storSD space.Our mainr esult is a r ndomized algor ithm for kMedian prE lem which p duces a constant factor appr oximation in one pass using storR4 space O(kpolylog n). This is a significant imp r vement of the prS ious best algor5 hm which yielded a 2 appr ximation using O(n )space.