# Approximation Algorithms for Facility Location Problems

## Abstract

One of the most flourishing areas of research in the design and analysis of approximation algorithms has been for facility location problems. In particular, for the metric case of two simple models, the uncapacitated facility location and the *k*-median problems, there are now a variety of techniques that yield constant performance guarantees. These methods include LP rounding, primal-dual algorithms, and local search techniques. Furthermore, the salient ideas in these algorithms and their analyzes are simple-to-explain and reflect a surprising degree of commonality. This note is intended as companion to our lecture at CONF 2000, mainly to give pointers to the appropriate references.

## Keywords

Local Search Approximation Algorithm Facility Location Local Search Algorithm Facility Location Problem## Preview

Unable to display preview. Download preview PDF.

## References

- 1.S. Arora, P. Raghavan, and S. Rao. Approximation schemes for Euclidean k-medians and related problems. In
*Proceedings of the 30th Annual ACM Symposium on Theory of Computing*, pages 106–113, 1998.Google Scholar - 2.M. L. Balinksi. On finding integer solutions to linear programs. In
*Proceedings of the IBM Scientific Computing Symposium on Combinatorial Problems*, pages 225–248. IBM, 1966.Google Scholar - 3.M. Charikar and S. Guha. Improved combinatorial algorithms for the facility loca-tion and k-median problems. In
*Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science*, pages 378–388, 1999.Google Scholar - 4.M. Charikar, S. Guha, É. Tardos, and D. B. Shmoys. A constant-factor approximation algorithms for the k-median problem. In
*Proceedings of the 31st Annual ACM Symposium on Theory of Computing*, pages 1–10, 1999.Google Scholar - 5.F. A. Chudak. Improved approximation algorithms for uncapacitated facility location. In R.E. Bixby, E.A. Boyd, and R.Z. Ríos-Mercado, editors,
*Integer Programming and Combinatorial Optimization*, volume 1412 of*Lecture Notes in Computer Science*, pages 180–194, Berlin, 1998. Springer.CrossRefGoogle Scholar - 6.F. A. Chudak and D. B Shmoys. Improved approximation algorithms for the uncapacitated facility location problem. Submitted for publication.Google Scholar
- 7.S. Guha and S. Khuller. Greedy strikes back: Improved facility location algorithms. In
*Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms*, pages 649–657, 1998.Google Scholar - 8.D. S. Hochbaum. Heuristics for the fixed cost median problem.
*Math.Programming*, 22:148–162, 1982.MATHCrossRefMathSciNetGoogle Scholar - 9.K. Jain and V. V. Vazirani. Primal-dual approximation algorithms for metric facility location and k-median problems. In
*Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science*, pages 2–13, 1999.Google Scholar - 10.M. R. Korupolu, C. G. Plaxton, and R. Rajaraman. Analysis of a local searchheuristic for facility location problems. In
*Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms*, pages 1–10, 1998.Google Scholar - 11.A. A. Kuehn and M. J. Hamburger. A heuristic program for locating warehouses.
*Management Sci.*, 9:643–666, 1963.CrossRefGoogle Scholar - 12.J.-H. Lin and J. S. Vitter. ∈-approximations with minimum packing constraint violation. In
*Proceedings of the 24th Annual ACM Symposium on Theory of Computing*, pages 771–782, 1992.Google Scholar - 13.J.-H. Lin and J. S. Vitter. Approximation algorithms for geometric median problems.
*Inform.Proc.Lett.*, 44:245–249, 1992.MATHCrossRefMathSciNetGoogle Scholar - 14.A. S. Manne. Plant location under economies-of-scale-decentralization and computation.
*Management Sci.*, 11:213–235, 1964.Google Scholar - 15.R. R. Mettu and C. G. Plaxton. The online median problem. In
*Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science*, 2000, to appear.Google Scholar - 16.P. Raghavan and C. D. Thompson. Randomized rounding: a technique for provably good algorithms and algorithmic proofs.
*Combinatorica*, 7:365–374, 1987.MATHCrossRefMathSciNetGoogle Scholar - 17.D. B. Shmoys, É. Tardos, and K. I. Aardal. Approximation algorithms for facility location problems. In
*Proceedings of the 29th Annual ACM Symposium on Theory of Computing*, pages 265–274, 1997.Google Scholar - 18.J. F. Stollsteimer.
*The effect of tec nical change and output expansion on the optimum number,size and location of pear marketing facilities in a California pear producing region*. PhD thesis, University of California at Berkeley, Berkeley, California, 1961.Google Scholar - 19.J. F. Stollsteimer. A working model for plant numbers and locations.
*J.Farm Econom.*, 45:631–645, 1963.CrossRefGoogle Scholar - 20.M. Thorup. Quick k-medians. Unpublished manuscript, 2000.Google Scholar