Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
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Improved Approximation Algorithms for Metric Facility Location Problems
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
SIAM Journal on Computing
A Multiexchange Local Search Algorithm for the Capacitated Facility Location Problem
Mathematics of Operations Research
Improved approximation for universal facility location
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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Efficient algorithms for the 2-gathering problem
ACM Transactions on Algorithms (TALG)
Importance sampling via load-balanced facility location
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Theoretical Computer Science
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Transactions on computational science IX
Approximate shortest path queries using Voronoi duals
Transactions on computational science IX
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We study the lower-bounded facility location problem, which generalizes the classical uncapacitated facility location problem in that it comes with lower bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [12] and by Guha, Meyerson, and Munagala [7], both of which give bicriteria approximation algorithms for it. These bicriteria algorithms come within a constant factor of the optimal solution cost, but they also violate the lower bound constraints by a constant factor. Our result in this paper is the first true approximation algorithm for the lower-bounded facility location problem, which respects the lower bound constraints and achieves a constant approximation ratio for the objective function. The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constant-factor approximation algorithms.