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52
Primaldual approximation algorithms for metric facility location and kmedian problems
 Journal of the ACM
, 1999
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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 215 (14 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 209 (14 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....
Efficient algorithms for geometric optimization
 ACM Comput. Surv
, 1998
"... We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear progra ..."
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Cited by 94 (12 self)
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We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other querytype problems.
An Efficient Distributed Algorithm for Constructing Small Dominating Sets
, 2001
"... The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node ..."
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Cited by 86 (1 self)
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The dominating set problem asks for a small subset D of nodes in a graph such that every node is either in D or adjacent to a node in D. This problem arises in a number of distributed network applications, where it is important to locate a small number of centers in the network such that every node is nearby at least one center. Finding a dominating set of minimum size is NPcomplete, and the best known approximation is logarithmic in the maximum degree of the graph and is provided by the same simple greedy approach that gives the wellknown logarithmic approximation result for the closely related set cover problem.
Achieving Anonymity via Clustering
 In PODS
, 2006
"... Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of deidentifying records is to remove identifying fields such as social security number, name etc. However, recent resea ..."
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Cited by 78 (1 self)
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Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of deidentifying records is to remove identifying fields such as social security number, name etc. However, recent research has shown that a large fraction of the US population can be identified using nonkey attributes (called quasiidentifiers) such as date of birth, gender, and zip code [15]. Sweeney [16] proposed the kanonymity model for privacy where nonkey attributes that leak information are suppressed or generalized so that, for every record in the modified table, there are at least k−1 other records having exactly the same values for quasiidentifiers. We propose a new method for anonymizing data records, where quasiidentifiers of data records are first clustered and then cluster centers are published. To ensure privacy of the data records, we impose the constraint
Exact and Approximation Algorithms for Clustering
, 1997
"... In this paper we present a n O(k 1\Gamma1=d ) time algorithm for solving the kcenter problem in R d , under L1 and L 2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete kcenter problem, as well. We also describe a simple (1 + ffl)approximation algorith ..."
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Cited by 57 (5 self)
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In this paper we present a n O(k 1\Gamma1=d ) time algorithm for solving the kcenter problem in R d , under L1 and L 2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete kcenter problem, as well. We also describe a simple (1 + ffl)approximation algorithm for the kcenter problem, with running time O(n log k) + (k=ffl) O(k 1\Gamma1=d ) . Finally, we present a n O(k 1\Gamma1=d ) time algorithm for solving the Lcapacitated kcenter problem, provided that L = \Omega\Gamma n=k 1\Gamma1=d ) or L = O(1). We conclude with a simple approximation algorithm for the Lcapacitated kcenter problem. The work on this paper was partially supported by a National Science Foundation Grant CCR9301259, by an Army Research Office MURI grant DAAH049610013, by a Sloan fellowship, by an NYI award and matching funds from Xerox Corporation, and by a grant from the U.S.Israeli Binational Science Foundation. y Department of Computer Science, Box ...
Fixedparameter algorithms for the (k, r)center in planar graphs and map graphs
 ACM TRANSACTIONS ON ALGORITHMS
, 2003
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The Capacitated KCenter Problem
 In Proceedings of the 4th Annual European Symposium on Algorithms, Lecture Notes in Computer Science 1136
, 1996
"... The capacitated Kcenter problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assign ..."
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Cited by 34 (5 self)
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The capacitated Kcenter problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NPhard. We give polynomial time approximation algorithms for two different versions of this problem that achieve approximation factors of 5 and 6. We also study some generalizations of this problem. 1. Introduction The basic Kcenter problem is a fundamental facility location problem [17] and is defined as follows: given an edgeweighted graph G = (V; E) find a subset S ` V of size at most K such that each vertex in V is "close" to some vertex in S. More formally, the objective function is defined as follows: min S`V max u2V min v2S d(u; v) where d is the distance function. For example, one may wish to install K fire stations and mi...