Abstract
We consider the facility location problem where each facility can serve at most U clients. We analyze a local search algorithm for this problem which uses only the operations of add, delete and swap and prove that any locally optimum solution is no more than 3 times the global optimum. This improves on a result of Chudak and Williamson who proved an approximation ratio of \(3+2\sqrt{2}\) for the same algorithm. We also provide an example which shows that our analysis is tight.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristics for k-median and facility location problems. SIAM J. Comput. 33(3), 544–562 (2004)
Chudak, F., Williamson, D.P.: Improved approximation algorithms for capacitated facility location problems. Math. Program. 102(2), 207–222 (2005)
Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. J. Algorithms 37(1), 146–188 (2000)
Mahdian, M., Pál, M.: Universal facility location. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 409–421. Springer, Heidelberg (2003)
Mahdian, M., Ye, Y., Zhang, J.: A 2-approximation algorithm for the soft-capacitated facility location problem. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 129–140. Springer, Heidelberg (2003)
Pál, M., Tardos, É., Wexler, T.: Facility location with nonuniform hard capacities. In: FOCS ’01: Proceedings of the 42nd IEEE symposium on Foundations of Computer Science, Washington, DC, USA, p. 329. IEEE Computer Society, Los Alamitos (2001)
Zhang, J., Chen, B., Ye, Y.: A multiexchange local search algorithm for the capacitated facility location problem. Math. Oper. Res. 30(2), 389–403 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aggarwal, A. et al. (2010). A 3-Approximation for Facility Location with Uniform Capacities. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-13036-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13035-9
Online ISBN: 978-3-642-13036-6
eBook Packages: Computer ScienceComputer Science (R0)