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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 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
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.
An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
, 2002
"... We design new approximation algorithm for the metric uncapacitated facility location problem. This algorithm is of LP rounding type and is based on a rounding technique developed in [57]. ..."
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Cited by 40 (3 self)
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We design new approximation algorithm for the metric uncapacitated facility location problem. This algorithm is of LP rounding type and is based on a rounding technique developed in [57].
Generalized submodular cover problems and applications
 Theoretical Computer Science
"... The greedy approach has been successfully applied in the past to produce logarithmic ratio approximations to NPhard problems under certain conditions. The problems for which these conditions hold are known as submodular cover problems. The current paper 1 extends the applicability of the greedy ap ..."
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Cited by 39 (13 self)
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The greedy approach has been successfully applied in the past to produce logarithmic ratio approximations to NPhard problems under certain conditions. The problems for which these conditions hold are known as submodular cover problems. The current paper 1 extends the applicability of the greedy approach to wider classes of problems. The usefulness of our extensions is illustrated by giving new approximate solutions for two dierent types of problems. The rst problem is that of nding the spanning tree of minimum weight among those whose diameter is bounded by D. A logarithmic ratio approximation algorithm is given for the cases of D = 4 and D = 5. This approximation ratio is also proved to be the best possible, unless P = NP. The second type involves some (known and new) center selection problems, for which new logarithmic ratio approximation algorithms are given. Again, it is shown that the ratio must be at least logarithmic unless P = NP.
KMedians, Facility Location, and the ChernoffWald Bound
, 2000
"... We study the general (nonmetric) facilitylocation and weighted kmedians problems, as well as the fractional facilitylocation and unweighted kmedians problems. We describe a natural randomized rounding scheme and use it to derive approximation algorithms for all of these problems. For facility l ..."
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Cited by 9 (4 self)
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We study the general (nonmetric) facilitylocation and weighted kmedians problems, as well as the fractional facilitylocation and unweighted kmedians problems. We describe a natural randomized rounding scheme and use it to derive approximation algorithms for all of these problems. For facility location and weighted kmedians, the respective algorithms are polynomialtime [Hk + d] and [(1 + )d; ln(n + n=)k]approximation algorithms. These performance guarantees improve on the best previous performance guarantees, due respectively to Hochbaum (1982) and Lin and Vitter (1992). For fractional kmedians, the algorithm is a new, Lagrangianrelaxation, [(1 + )d; (1 + )k]