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38
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 236 (13 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 220 (13 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 114 (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.
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 94 (2 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(k1�1=d) time algorithm for solving the kcenter problem in R d, under L1 and L2 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 +)approximation algorithm for the kcenter pr ..."
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Cited by 71 (5 self)
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In this paper we present a n O(k1�1=d) time algorithm for solving the kcenter problem in R d, under L1 and L2 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 +)approximation algorithm for the kcenter problem, with running time O(n log k) + (k = ) O(k1�1=d). Finally, we present a n O(k1�1=d) time algorithm for solving the Lcapacitated kcenter problem, provided that L = (n=k 1�1=d) or L = O(1). We conclude with a simple approximation algorithm for the Lcapacitated kcenter problem.
A MultiExchange Local Search Algorithm for the Capacitated Facility Location Problem
 Mathematics of Operations Research
, 2004
"... We present a multiexchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the per ..."
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Cited by 27 (0 self)
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We present a multiexchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between 3+ 2 # 2 # and 3+ 2 # 2+ # for any given constant # > 0. Previously known best approximation ratio for the CFLP is 7.88, due to Mahdian and Pal (2003), based on the operations proposed by Pal, Tardos and Wexler (2001).
Continuous Weber and kMedian Problems
, 2000
"... We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the "continuous kmedian (Weber) problem" where the goal is to select one or more center points that minimize the ..."
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Cited by 13 (2 self)
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We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the "continuous kmedian (Weber) problem" where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed as an integral over the relevant region, versus the usual discrete sum of distances. The resulting facility location problems are inherently geometric, requiring analysis techniques of computational geometry. We provide polynomialtime algorithms for various versions of the L1 1median (Weber) problem. We also consider the multiplecenter version of the L1 kmedian problem, which we prove is NPhard for large k.
Facility Location with Dynamic Distance Functions
"... Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating in ..."
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Cited by 5 (1 self)
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Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to traffic congestion the traversal time on links changes with time. Very often, we have some estimates as to how the edge lengths change over time, and our objective is to choose a set of locations (vertices) as centers, such that at every time instant each vertex has a center close to it (clearly, the center close to a vertex may change over time). We also provide approximation algorithms as well as hardness results for the Kcenter problem under this model. This is the first comprehensive study regarding approximation algorithms for facility location for good timeinvariant solutions. 1. Introduction Previous theoretical work on fac...