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23
Primaldual approximation algorithms for metric facility location and kmedian problems
 Journal of the ACM
, 1999
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Greedy strikes back: Improved facility location algorithms
 Journal of Algorithms
, 1999
"... A fundamental facility location problem is to choose the location of facilities, such as industrial plants and warehouses, to minimize the cost of satisfying the demand for some commodity. There are associated costs for locating the facilities, as well as transportation costs for distributing the co ..."
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Cited by 183 (12 self)
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A fundamental facility location problem is to choose the location of facilities, such as industrial plants and warehouses, to minimize the cost of satisfying the demand for some commodity. There are associated costs for locating the facilities, as well as transportation costs for distributing the commodities. We assume that the transportation costs form a metric. This problem is commonly referred to as the uncapacitated facility location (UFL) problem. Applications to bank account location and clustering, as well as many related pieces of work, are discussed by Cornuejols, Nemhauser and Wolsey [2]. Recently, the first constant factor approximation algorithm for this problem was obtained by Shmoys, Tardos and Aardal [16]. We show that a simple greedy heuristic combined with the algorithm by Shmoys, Tardos and Aardal, can be used to obtain an approximation guarantee of 2.408. We discuss a few variants of the problem, demonstrating better approximation factors for restricted versions of the problem. We also show that the problem is Max SNPhard. However, the inapproximability constants derived from the Max SNP hardness are very close to one. By relating this problem to Set Cover, we prove a lower bound of 1.463 on the best possible approximation ratio assuming NP / ∈ DT IME[n O(log log n)]. 1
Greedy Facility Location Algorithms analyzed using Dual Fitting with FactorRevealing LP
 Journal of the ACM
, 2001
"... 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 c ..."
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Cited by 101 (13 self)
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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.
Algorithms for Facility Location Problems with Outliers (Extended Abstract)
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms
, 2000
"... ) Moses Charikar Samir Khuller y David M. Mount z Giri Narasimhan x Abstract Facility location problems are traditionally investigated with the assumption that all the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called outlier ..."
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Cited by 67 (7 self)
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) Moses Charikar Samir Khuller y David M. Mount z Giri Narasimhan x Abstract Facility location problems are traditionally investigated with the assumption that all the clients are to be provided service. A significant shortcoming of this formulation is that a few very distant clients, called outliers, can exert a disproportionately strong influence over the final solution. In this paper we explore a generalization of various facility location problems (Kcenter, Kmedian, uncapacitated facility location etc) to the case when only a specified fraction of the customers are to be served. What makes the problems harder is that we have to also select the subset that should get service. We provide generalizations of various approximation algorithms to deal with this added constraint. 1 Introduction The facility location problem and the related clustering problems, kmedian and kcenter, are widely studied in operations research and computer science [3, 7, 22, 24, 32]. Typically in...
Universal Facility Location
 in Proc. of ESA ’03
, 2003
"... In the Universal Facility Location problem we are given a set of demand points and a set of facilities. ..."
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Cited by 26 (0 self)
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In the Universal Facility Location problem we are given a set of demand points and a set of facilities.
Using linear programming in the design and analysis of approximation algorithms: two illustrative problems
 Approximation Algorithms for Combinatorial Optimization, K. Jansen and J. Rolim (Eds
, 1998
"... One of the foremost techniques in the design and analysis of approximation algorithms is to round the optimal solution to a linear programming relaxation in order to compute a nearoptimal solution to the problem at hand. We shall survey recent work in this vein for two particular problems: the un ..."
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Cited by 7 (0 self)
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One of the foremost techniques in the design and analysis of approximation algorithms is to round the optimal solution to a linear programming relaxation in order to compute a nearoptimal solution to the problem at hand. We shall survey recent work in this vein for two particular problems: the uncapacitated facility location problem and the problem of scheduling precedenceconstrained jobs on one machine so as to minimize a weighted average of their completion times.
Finding Facilities Fast
, 2008
"... Clustering can play a critical role in increasing the performance and lifetime of wireless networks. The facility location problem is a general abstraction of the clustering problem and this paper presents the first constantfactor approximation algorithm for the facility location problem on unit di ..."
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Cited by 4 (0 self)
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Clustering can play a critical role in increasing the performance and lifetime of wireless networks. The facility location problem is a general abstraction of the clustering problem and this paper presents the first constantfactor approximation algorithm for the facility location problem on unit disk graphs (UDGs), a commonly used model for wireless networks. In this version of the problem, connection costs are not metric, i.e., they do not satisfy the triangle inequality, because connecting to a nonneighbor costs ∞. In nonmetric settings the best approximation algorithms guarantee an O(log n)factor approximation, but we are able to use structural properties of UDGs to obtain a constantfactor approximation. Our approach combines ideas from the primaldual algorithm for facility location due to Jain and Vazirani (JACM, 2001) with recent results on the weighted minimum dominating set problem for UDGs (Huang et al., J. Comb. Opt., 2008). We then show that the facility location problem on UDGs is inherently local and one can solve local subproblems independently and combine the solutions in a simple way to obtain a good solution to the overall problem. This leads to a distributed version of our algorithm in the LOCAL model that runs in constant rounds and still yields a constantfactor approximation. Even if the UDG is specified without geometry, we are able to combine recent results on maximal independent sets and clique partitioning of UDGs, to obtain an O(log n)approximation that runs in O(log ∗ n) rounds.
Primaldual variable neighborhood search for the simple plant location problem
 INFORMS Journal on Computing
"... doi 10.1287/ijoc.1060.0196 ..."