New Approximation Algorithms for the Unsplittable Capacitated Facility Location Problem

  • Babak Behsaz
  • Mohammad R. Salavatipour
  • Zoya Svitkina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

Abstract

In this paper, we consider the Unsplittable (hard) Capacitated Facility Location Problem (UCFLP) with uniform capacities and present some new approximation algorithms for it. This problem is a generalization of the classical facility location problem where each facility can serve at most u units of demand and each client must be served by exactly one facility. It is known that it is NP-hard to approximate this problem within any factor without violating the capacities. So we consider bicriteria (α,β)-approximations where the algorithm returns a solution whose cost is within factor α of the optimum and violates the capacity constraints within factor β. We present a framework for designing bicriteria approximation algorithms and show two new approximation algorithms with factors (10.173,3/2) and (30.432,4/3). These are the first algorithms with constant approximation in which the violation of capacities is below 2. The heart of our algorithms is a reduction from the UCFLP to a restricted version of the problem. One feature of this reduction is that any (O(1),1 + ε)-approximation for the restricted version implies an (O(1),1 + ε)-approximation for the UCFLP for any constant ε > 0 and we believe our techniques might be useful towards finding such approximations or perhaps (f(ε),1 + ε)-approximation for the UCFLP for some function f. In addition, we present a quasi-polynomial time (1 + ε,1 + ε)-approximation for the (uniform) UCFLP in Euclidean metrics, for any constant ε > 0.

Keywords

approximation algorithms unsplittable capacitated facility location problem Euclidean metrics 

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References

  1. 1.
    Aggarwal, A., Anand, L., Bansal, M., Garg, N., Gupta, N., Gupta, S., Jain, S.: A 3-Approximation for Facility Location with Uniform Capacities. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol. 6080, pp. 149–162. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Arora, S.: Polynomial time approximation schemes for euclidean tsp and other geometric problems. In: Proceedings of the 37th Annual Symposium on Foundations of Computer Science. pp. 2–12 (1996)Google Scholar
  3. 3.
    Bateni, M., Hajiaghayi, M.: Assignment problem in content distribution networks: unsplittable hard-capacitated facility location. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 805–814 (2009)Google Scholar
  4. 4.
    Guha, S., Khuller, S.: Greedy strikes back: improved facility location algorithms. In: SODA 1998: Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 649–657 (1998)Google Scholar
  5. 5.
    Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. In: Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1998, pp. 1–10 (1998)Google Scholar
  6. 6.
    Li, S.: A 1.488 Approximation Algorithm for the Uncapacitated Facility Location Problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 77–88. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Shmoys, D., Tardos, E.: An approximation algorithm for the generalized assignment problem. Mathematical Programming 62(3), 461–474 (1993)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Shmoys, D., Tardos, E., Aardal, K.: Approximation algorithms for facility location problems. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 265–274 (1997)Google Scholar
  10. 10.
    Zhang, J., Chen, B., Ye, Y.: A Multi-exchange Local Search Algorithm for the Capacitated Facility Location Problem. In: Bienstock, D., Nemhauser, G.L. (eds.) IPCO 2004. LNCS, vol. 3064, pp. 219–233. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Babak Behsaz
    • 1
  • Mohammad R. Salavatipour
    • 1
  • Zoya Svitkina
    • 2
  1. 1.Dept. of Computing Sci.Univ. of AlbertaEdmontonCanada
  2. 2.Google Inc.Mountain ViewUSA

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