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Universal Facility Location

  • Mohammad Mahdian
  • Martin Pál
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2832)

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.

Keywords

Facility Location Local Search Algorithm Facility Location Problem Demand Point Local Search Heuristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    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)Google Scholar
  2. 2.
    Balinski, M.L.: On finding integer solutions to linear programs. In: Proc. IBM Scientific Computing Symposium on Combinatorial Problems, pp. 225–248 (1966)Google Scholar
  3. 3.
    Bauer, P., Enders, R.: A capacitated facility location problem with integer decision variables. In: International Symposium on Math. Programming (1997)Google Scholar
  4. 4.
    Charikar, M., Guha, S.: Improved combinatorial algorithms for facility location and k-median problems. In: Proceedings of FOCS 1999, pp. 378–388 (1999)Google Scholar
  5. 5.
    Christofides, N., Beasley, J.E.: An algorithm for the capacitated warehouse location problem. European Journal of Operational Research 12, 19–28 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Feldman, E., Lehrer, F.A., Ray, T.L.: Warehouse locations under continuous economies of scale. Management Science 12, 670–684 (1966)CrossRefGoogle Scholar
  8. 8.
    Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Hajiaghayi, M., Mahdian, M., Mirrokni, V.S.: The facility location problem with general cost functions. Networks 42(1), 42–47 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    Kaufman, L., Eede, M.V., Hansen, P.: A plant and warehouse location problem. Operations Research Quarterly 28, 547–554 (1977)zbMATHCrossRefGoogle Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    Kuehn, A.A., Hamburger, M.J.: A heuristic program for locating warehouses. Management Science 9, 643–666 (1963)CrossRefGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    Nauss, R.M.: An improved algorithm for the capacitated facility location problem. Journal of Operational Research Society 29, 1195–1202 (1978)zbMATHGoogle Scholar
  18. 18.
    Pál, M., Tardos, E., Wexler, T.: Facility location with hard capacities. In: Proceedings of the 42nd Annual Symposium on Foundations of Computer Science (2001)Google Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Stollsteimer, J.F.: A working model for plant numbers and locations. J. Farm Econom. 45, 631–645 (1963)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mohammad Mahdian
    • 1
  • Martin Pál
    • 2
  1. 1.Laboratory for Computer ScienceMITCambridgeUSA
  2. 2.Computer Science DepartmentCornell UniversityIthacaUSA

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