Abstract
In the Universal Facility Location problem we are given a set of demand points and a set of facilities. The goal is to assign the demands to facilities in such a way that the sum of service and facility costs is minimized. The service cost is proportional to the distance each unit of demand has to travel to its assigned facility, whereas the facility cost of each facility i depends on the amount of demand assigned to that facility and is given by a cost function f i (·). We present a (7.88 + ε)-approximation algorithm for the Universal Facility Location problem based on local search, under the assumption that the cost functions f i are nondecreasing. The algorithm chooses local improvement steps by solving a knapsack-like subproblem using dynamic programming. This is the first constant-factor approximation algorithm for this problem. Our algorithm also slightly improves the best known approximation ratio for the capacitated facility location problem with non-uniform hard capacities.
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. In: Proceedings of 33rd ACM Symposium on Theory of Computing (2001)
Balinski, M.L.: On finding integer solutions to linear programs. In: Proc. IBM Scientific Computing Symposium on Combinatorial Problems, pp. 225–248 (1966)
Bauer, P., Enders, R.: A capacitated facility location problem with integer decision variables. In: International Symposium on Math. Programming (1997)
Charikar, M., Guha, S.: Improved combinatorial algorithms for facility location and k-median problems. In: Proceedings of FOCS 1999, pp. 378–388 (1999)
Christofides, N., Beasley, J.E.: An algorithm for the capacitated warehouse location problem. European Journal of Operational Research 12, 19–28 (1983)
Chudak, F.A., Williamson, D.P.: Improved approximation algorithms for capacitated facility location problems. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, pp. 99–113. Springer, Heidelberg (1999)
Feldman, E., Lehrer, F.A., Ray, T.L.: Warehouse locations under continuous economies of scale. Management Science 12, 670–684 (1966)
Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)
Guha, S., Meyerson, A., Munagala, K.: Hierarchical placement and network design problems. In: Proceedings of the 41th Annual IEEE Symposium on Foundations of Computer Science (2000)
Hajiaghayi, M., Mahdian, M., Mirrokni, V.S.: The facility location problem with general cost functions. Networks 42(1), 42–47 (2003)
Karger, D., Minkoff, M.: Building Steiner trees with incomplete global knowledge. In: Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science (2000)
Kaufman, L., Eede, M.V., Hansen, P.: A plant and warehouse location problem. Operations Research Quarterly 28, 547–554 (1977)
Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. In: Proceedings of the 9th Annual ACMSIAM Symposium on Discrete Algorithms, January 1998, pp. 1–10 (1998)
Kuehn, A.A., Hamburger, M.J.: A heuristic program for locating warehouses. Management Science 9, 643–666 (1963)
Mahdian, M., Ye, Y., Zhang, J.: Improved approximation algorithms for metric facility location problems. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, Springer, Heidelberg (2002)
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)
Nauss, R.M.: An improved algorithm for the capacitated facility location problem. Journal of Operational Research Society 29, 1195–1202 (1978)
Pál, M., Tardos, E., Wexler, T.: Facility location with hard capacities. In: Proceedings of the 42nd Annual Symposium on Foundations of Computer Science (2001)
Shmoys, D.B.: Approximation algorithms for facility location problems. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 27–33. Springer, Heidelberg (2000)
Stollsteimer, J.F.: A working model for plant numbers and locations. J. Farm Econom. 45, 631–645 (1963)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mahdian, M., Pál, M. (2003). Universal Facility Location. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-39658-1_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20064-2
Online ISBN: 978-3-540-39658-1
eBook Packages: Springer Book Archive