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11
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 ..."
Abstract

Cited by 100 (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.
Faulttolerant facility location
 in Proceedings of the 14th Annual ACMSIAM Symposium on Discrete Algorithms
, 2003
"... We study a faulttolerant generalization of the classical uncapacitated facility location problem. We want to open a subset of facilities from a given set F and assign each client j in a given set D to rj ≥ 1 distinct open facilities so as to minimize the sum of the facility opening costs and the cl ..."
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Cited by 19 (3 self)
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We study a faulttolerant generalization of the classical uncapacitated facility location problem. We want to open a subset of facilities from a given set F and assign each client j in a given set D to rj ≥ 1 distinct open facilities so as to minimize the sum of the facility opening costs and the client assignment costs. We also consider the faulttolerant kmedian problem where instead of facility costs we are given a number k of facilities that may be opened, and the objective is to minimize only the assignment cost. Multiple facilities provide a safeguard against failures. If the facility closest to a client ‘fails’, the other facilities assigned to it could be used to serve it, e.g., in designing a network involving the placement of caches or routers, one would like to connect a client to multiple caches or routers so as to be resistant under node or link failures. We consider the case where the distances, cij, formametric.
Designing overlay multicast networks for streaming
 In Proceedings of ACM Symposium on Parallel Algorithms and Architectures
, 2003
"... In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that ..."
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Cited by 16 (4 self)
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In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that our algorithm applies to includes the one used by Akamai Technologies to deliver live media streams over the Internet. In particular, we analyze networks consisting of three stages of nodes. The nodes in the first stage are the sources where live streams originate. A source forwards each of its streams to one or more nodes in the second stage, which are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage, which are called the sinks. As the packets in a stream travel from one stage to the next, some of them may be lost. The job of a sink is to combine the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. We assume that the loss rate between any pair of nodes in the network is known, and that losses between different pairs are independent, but discuss extensions in which some losses may be correlated.
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 used only ..."
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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...
ROBUST FAULT TOLERANT UNCAPACITATED FACILITY LOCATION
, 2010
"... In the uncapacitated facility location problem, given a graph, a set of demands and opening costs, it is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities. This paper concerns th ..."
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Cited by 4 (0 self)
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In the uncapacitated facility location problem, given a graph, a set of demands and opening costs, it is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities. This paper concerns the robust faulttolerant version of the uncapacitated facility location problem (RFTFL). In this problem, one or more facilities might fail, and each demand should be supplied by the closest open facility that did not fail. It is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities that did not fail, after the failure of up to α facilities. We present a polynomial time algorithm that yields a 6.5approximation for this problem with at most one failure and a 1.5 + 7.5αapproximation for the problem with at most α> 1 failures. We also show that the RFTFL problem is NPhard even on trees, and even in the case of a single failure.
Faulttolerant facility location: a randomized dependent LProunding algorithm. arXiv:1003.1295v1
"... Abstract. We give a new randomized LProunding 1.725approximation algorithm for the metric FaultTolerant Uncapacitated Facility Location problem. This improves on the previously best known 2.076approximation algorithm of Swamy & Shmoys. To the best of our knowledge, our work provides the first ap ..."
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Cited by 2 (0 self)
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Abstract. We give a new randomized LProunding 1.725approximation algorithm for the metric FaultTolerant Uncapacitated Facility Location problem. This improves on the previously best known 2.076approximation algorithm of Swamy & Shmoys. To the best of our knowledge, our work provides the first application of a dependentrounding technique in the domain of facility location. The analysis of our algorithm benefits from, and extends, methods developed for Uncapacitated Facility Location; it also helps uncover new properties of the dependentrounding approach. An important concept that we develop is a novel, hierarchical clustering scheme. Typically, LProunding approximation algorithms for facility location problems are based on partitioning facilities into disjoint clusters and opening at least one facility in each cluster. We extend this approach and construct a laminar family of clusters, which then guides the rounding procedure: this allows us to exploit properties of dependent rounding, and provides a quite tight analysis resulting in the improved approximation ratio. 1
An Optimized Clustering and Selective Probing Framework to Support Internet QualityofService Routing
, 2006
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