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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 227 (11 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....
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 221 (11 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
Analysis of a local search heuristic for facility location problems
 IN PROCEEDINGS OF THE 9TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1998
"... In this paper, we study approximation algorithms for several NPhard facility location problems. We prove that a simple local search heuristic yields polynomialtime constantfactor approximation bounds for the metric versions of the uncapacitated kmedian problem and the uncapacitated facility loca ..."
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Cited by 158 (4 self)
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In this paper, we study approximation algorithms for several NPhard facility location problems. We prove that a simple local search heuristic yields polynomialtime constantfactor approximation bounds for the metric versions of the uncapacitated kmedian problem and the uncapacitated facility location problem. (For the kmedian problem, our algorithms require a constantfactor blowup in the parameter k.) This local search heuristic was rst proposed several decades ago, and has been shown to exhibit good practical performance in empirical studies. We also extend the above results to obtain constantfactor approximation bounds for the metric versions of capacitated kmedian and facility location problems.
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 148 (12 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.
A new greedy approach for facility location problems
"... We present a simple and natural greedy algorithm for the metric uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73. Furthermore, we will show that our algorithm has a property which allows us to apply the technique of Lagra ..."
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Cited by 143 (9 self)
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We present a simple and natural greedy algorithm for the metric uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73. Furthermore, we will show that our algorithm has a property which allows us to apply the technique of Lagrangian relaxation. Using this property, we can nd better approximation algorithms for many variants of the facility location problem, such as the capacitated facility location problem with soft capacities and a common generalization of the kmedian and facility location problem. We will also prove a lower bound on the approximability of the kmedian problem.
Fast approximate energy minimization with label costs
, 2010
"... The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simult ..."
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Cited by 108 (9 self)
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The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simultaneously optimize “label costs ” as well. An energy with label costs can penalize a solution based on the set of labels that appear in it. The simplest special case is to penalize the number of labels in the solution. Our energy is quite general, and we prove optimality bounds for our algorithm. A natural application of label costs is multimodel fitting, and we demonstrate several such applications in vision: homography detection, motion segmentation, and unsupervised image segmentation. Our C++/MATLAB implementation is publicly available.
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 90 (9 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...
The Online Median Problem
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... We introduce a natural variant of the (metric uncapacitated) kmedian problem that we call the online median problem. Whereas the kmedian problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities ar ..."
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Cited by 84 (2 self)
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We introduce a natural variant of the (metric uncapacitated) kmedian problem that we call the online median problem. Whereas the kmedian problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities are placed one at a time; a facility cannot be moved once it is placed, and the total number of facilities to be placed, k, is not known in advance. The objective of an online median algorithm is to minimize the competitive ratio, that is, the worstcase ratio of the cost of an online placement to that of an optimal offline placement. Our main result is a lineartime constantcompetitive algorithm for the online median problem. In addition, we present a related, though substantially simpler, lineartime constantfactor approximation algorithm for the (metric uncapacitated) facility location problem. The latter algorithm is similar in spirit to the recent primaldualbased facility location algorithm of Jain and Vazirani, but our approach is more elementary and yields an improved running time.
Placement Algorithms for Hierarchical Cooperative Caching
, 1999
"... Consider a hierarchical network in which each node periodically issues a request for an object drawn from a fixed set of unitsize objects. Suppose further that the following conditions are satisfied: the frequency with which each node accesses each object is known; each node has a cache of known ca ..."
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Cited by 70 (9 self)
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Consider a hierarchical network in which each node periodically issues a request for an object drawn from a fixed set of unitsize objects. Suppose further that the following conditions are satisfied: the frequency with which each node accesses each object is known; each node has a cache of known capacity; any cache can be accessed by any node; any request is satisfied by the closest node with a copy of the desired object, at a cost proportional to the distance between the accessing node and the closest copy. In such an environment, it is desirable to fill the available cache space with copies of objects in such a way that the average access cost is minimized. We provide both exact and approximate polynomialtime algorithms for this hierarchical placement problem. Our exact algorithm is based on a reduction to mincost flow, and does not appear to be practical for large problem sizes. Thus we are motivated to search for a faster approximation algorithm. Our main result is a simple constantfactor approximation algorithm for the hierarchical placement problem that admits an efficient distributed implementation.