Non-metric Multicommodity and Multilevel Facility Location

  • Rudolf Fleischer
  • Jian Li
  • Shijun Tian
  • Hong Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4041)


We give logarithmic approximation algorithms for the non-metric uncapacitated multicommodity and multilevel facility location problems. The former algorithms are optimal up to a constant factor, the latter algorithm is far away from the lower bound, but it is the first algorithm to solve the general multilevel problem. To solve the multicommodity problem, we also define a new problem, the friendly tour operator problem, which we approximate by a greedy algorithm.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aardal, K.: On the solution of one and two-level capacitated facility location problems by the cutting plane approach. Ph.D. thesis, Université Catholique de Louvain, Louvain-la-Neuve, Belgium (1992)Google Scholar
  2. 2.
    Aardal, K., Chudak, F.A., Shmoys, D.B.: A 3-approximation algorithm for the k-level uncapacitated facility location problem. Information Processing Letters 72(5-6), 161–167 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Aardal, K., Labbé, M., Leung, J., Queyranne, M.: On the two-level uncapacitated facility location problem. INFORMS Journal on Computing 8, 289–301 (1996)zbMATHCrossRefGoogle Scholar
  4. 4.
    Chvátal, V.: A greedy heuristic for the set cover problem. Mathematics of Operations Research 4, 233–235 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Feige, U.: A threshold of ln n for approximating set-cover. Journal of the ACM 45(4), 634–652 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Guha, S., Khuller, S.: Improved methods for approximating node weighted Steiner trees and connected dominating sets. Information and Computation 150, 57–74 (1999)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Hochbaum, D.S.: Heuritics for the fixed cost median problem. Mathematical Programming 22(2), 148–162 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kaufmann, L., van den Eede, M., Hansen, P.: A plant and warehouse location problem. Operational Research Quaterly 28, 547–557 (1977)CrossRefGoogle Scholar
  10. 10.
    Mahdian, M., Ye, Y., Zhang, J.: A 1.52-approximation algorithm for the uncapacitated facility location problem. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 127–137. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Mirchandani, P., Francis, R. (eds.): Discrete Location Theory. John Wiley & Sons, Inc., Chichester (1990)zbMATHGoogle Scholar
  12. 12.
    Ravi, R., Sinha, A.: Multicommodity facility location. In: Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 342–349 (2004)Google Scholar
  13. 13.
    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
  14. 14.
    Shmoys, D.B., Swamy, C., Levi, R.: Facility location with service installation costs. In: Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 1088–1097 (2004)Google Scholar
  15. 15.
    Shmoys, D.B., Tardos, E., Aardal, K.I.: Approximation algorithms for facility location problems. In: Proceedings of the 29th ACM Symposium on the Theory of Computation (STOC 1997), pp. 265–274 (1997)Google Scholar
  16. 16.
    Tcha, D., Lee, B.: A branch-and-bound algorithm for the multi-level uncapacitated location problem. European Journal on Operations Research 18, 35–43 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Vygen, J.: Approximation Algorithms for Facility Location Problems (Lecture Notes). Technical Report Report No. 05950-OR, Research Institute for Discrete Mathematics, University of Bonn (2005)Google Scholar
  18. 18.
    Zhang, J.: Approximating the two-level facility location problem via a quasi-greedy approach. In: Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 808–817 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rudolf Fleischer
    • 1
  • Jian Li
    • 1
  • Shijun Tian
    • 1
  • Hong Zhu
    • 1
  1. 1.Department of Computer Science and Engineering, Shanghai Key Laboratory of Intelligent Information ProcessingFudan UniversityShanghaiChina

Personalised recommendations