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Improved Approximation Algorithms for Metric Facility Location Problems
 In Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
, 2002
"... In this paper we present a 1.52approximation algorithm for the metric uncapacitated facility location problem, and a 2approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for ..."
Abstract

Cited by 112 (11 self)
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In this paper we present a 1.52approximation algorithm for the metric uncapacitated facility location problem, and a 2approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our softcapacitated facility location algorithm achieves the integrality gap of the standard LP relaxation of the problem. Furthermore, we will show, using a result of Thorup, that our algorithms can be implemented in quasilinear time.
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.
Online Facility Location
"... We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized online O(1)competitive algorithm in the case where points arrive in random order. If points are ordered adversar ..."
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Cited by 53 (4 self)
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We consider the online variant of facility location, in which demand points arrive one at a time and we must maintain a set of facilities to service these points. We provide a randomized online O(1)competitive algorithm in the case where points arrive in random order. If points are ordered adversarially, we show that no algorithm can be constantcompetitive, and provide an O(log n)competitive algorithm. Our algorithms are randomized and the analysis depends heavily on the concept of expected waiting time. We also combine our techniques with those of Charikar and Guha to provide a lineartime constant approximation for the offline facility location problem.
The Facility Location Problem with General Cost Functions
 Networks
, 2002
"... In this paper we introduce a generalized version of the facility location problem in which the facility cost is a function of the number of clients assigned to the facility. We focus on the case of concave facility cost functions. We observe that this problem can be reduced to the uncapacitated faci ..."
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Cited by 24 (4 self)
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In this paper we introduce a generalized version of the facility location problem in which the facility cost is a function of the number of clients assigned to the facility. We focus on the case of concave facility cost functions. We observe that this problem can be reduced to the uncapacitated facility location problem. We analyze a natural greedy algorithm for this problem and show that its approximation factor is at most 1.861. We also consider several generalizations and variants of this problem.
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.
A 2Approximation Algorithm for the SoftCapacitated Facility Location Problem
 Proceedings of the 6th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX), LNCS 2764
, 2003
"... This paper is divided into two parts. In the first part of this paper, we present a 2approximation algorithm for the softcapacitated facility location problem. This achieves the integrality gap of the natural LP relaxation of the problem. The algorithm is based on an improved analysis of an algo ..."
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Cited by 15 (4 self)
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This paper is divided into two parts. In the first part of this paper, we present a 2approximation algorithm for the softcapacitated facility location problem. This achieves the integrality gap of the natural LP relaxation of the problem. The algorithm is based on an improved analysis of an algorithm for the linear facility location problem, and a bifactor approximatereduction from this problem to the softcapacitated facility location problem. We will define and use the concept of bifactor approximate reductions to improve the approximation factor of several other variants of the facility location problem. In the second part of the paper, we present an alternative analysis of the authors' 1.52approximation algorithm for the uncapacitated facility location problem, using a single factorrevealing LP. This answers an open question of [18]. Furthermore, this analysis, combined with a recent result of Thorup [25] shows that our algorithm can be implemented in quasilinear time, achieving the best known approximation factor in the best possible running time.