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18
Primaldual approximation algorithms for metric facility location and kmedian problems
 Journal of the ACM
, 1999
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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 104 (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.
CostDistance: Two Metric Network Design
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the numbe ..."
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Cited by 63 (7 self)
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Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the number of sources. We reduce many common network design problems to CostDistance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include singlesink buyatbulk with variable pipe types between different sets of nodes, facility location with buyatbulk type costs on edges, and maybecast with combind cost and distance metrics. Our algorithm is also the algorithm of choice for several previous network design problems, due to its ease of implementation and fast running time. 1 Introduction Consider designing a network from the ground up. We are given a set of customers, and need to place various servers and network links in order to cheaply provide sufficient service. If we only need to place the servers, this becomes the facility location problem and constantapproximations are known. If a single server handles all customers, and we impose the additional constraint that the set of available network link types is the same for every pair of nodes (subject to constant scaling factors on cost) then this is the single sink buyatbulk problem. We give the first known approximation for the general version of this problem with both servers and network links. We reduce the network design problem to an elegant theoretical framework: the CostDistance problem. We are given a graph with a single distinguished sink node (server). Every edge in this graph can be measured along two metrics; the first will be called cost and the second will be length. Note that the two metrics are entirely independent, and that there may be any number of parallel edges in the graph. We are given a set of sources (customers). Our objective is to construct a Steiner tree connecting the sources to the sink while minimizing the combined sum of the cost of the edges in the tree and sum over sources of the weighted length from source to sink.
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 27 (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.
On the TwoLevel Uncapacitated Facility Location Problem
 INFORMS J. COMPUT
, 1996
"... We study the twolevel uncapacitated facility location (TUFL) problem. Given two types of facilities, which we call yfacilities and zfacilities, the problem is to decide which facilities of both types to open, and to which pair of y and zfacilities each client should be assigned, in order to sat ..."
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Cited by 17 (3 self)
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We study the twolevel uncapacitated facility location (TUFL) problem. Given two types of facilities, which we call yfacilities and zfacilities, the problem is to decide which facilities of both types to open, and to which pair of y and zfacilities each client should be assigned, in order to satisfy the demand at maximum profit. We first present two multicommodity flow formulations of TUFL and investigate the relationship between these formulations and similar formulations of the onelevel uncapacitated facility location (UFL) problem. In particular, we show that all nontrivial facets for UFL define facets for the twolevel problem, and derive conditions when facets of TUFL are also facets for UFL. For both formulations of TUFL, we introduce new families of facets and valid inequalities and discuss the associated separation problems. We also characterize the extreme points of the LPrelaxation of the first formulation. While the LPrelaxation of a multicommodity formulation provi...
Improved Algorithms for Fault Tolerant Facility Location
 In Symposium on Discrete Algorithms
, 2001
"... We consider a generalization of the classical facility location problem, where we require the solution to be faulttolerant. Every demand point j is served by r j facilities instead of just one. The facilities other than the closest one are "backup" facilities for that demand, and will be ..."
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Cited by 9 (2 self)
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We consider a generalization of the classical facility location problem, where we require the solution to be faulttolerant. Every demand point j is served by r j facilities instead of just one. The facilities other than the closest one are "backup" facilities for that demand, and will be used only if the closer facility (or the link to it) fails. Hence, for any demand, we assign nonincreasing weights to the routing costs to farther facilities. The cost of assignment for demand j is the weighted linear combination of the assignment costs to its r j closest open facilities. We wish to minimize the sum of the cost of opening the facilities and the assignment cost of each demand j. We obtain a factor 4 approximation to this problem through the application of various rounding techniques to the linear relaxation of an integer program formulation. We further improve this...
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 5 (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.