Advertisement

An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem

  • Maxim Sviridenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2337)

Abstract

We design a new approximation algorithm for the metric uncapacitated facility location problem. This algorithm is of LP rounding type and is based on a rounding technique developed in [5,6,7].

Keywords

Approximation Algorithm Facility Location Facility Location Problem Demand Point Linear Programming Relaxation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. Aardal, F. Chudak and D. Shmoys, A 3-approximation algorithm for the k-level uncapacitated facility location problem, Inform. Process. Lett. 72 (1999), 161–167.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    A. Ageev, An approximation scheme for the uncapacitated facility location problem on planar graphs, manuscript.Google Scholar
  3. 3.
    A. Ageev and V. Beresnev, Polynomially solvable special cases of the simple plant location problem, in: R. Kannan and W. Pulleyblank (eds.), Proceedings of the First IPCO Conference, Waterloo University Press, Waterloo, 1990, 1–6.Google Scholar
  4. 4.
    A. Ageev and M. Sviridenko, An 0.828-approximation algorithm for the uncapacitated facility location problem, Discrete Appl. Math. 93 (1999), 149–156.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    A. Ageev and M. Sviridenko, Approximation algorithms for maximum coverage and max cut with given sizes of parts, Integer programming and combinatorial optimization (Graz, 1999), 17–30, Lecture Notes in Comput. Sci., 1610, Springer, Berlin, 1999.CrossRefGoogle Scholar
  6. 6.
    A. Ageev, R Hassin and M. Sviridenko, An 0.5-Approximation Algorithm for the MAX DICUT with given sizes of parts, SIAM Journal of Discrete Mathematics v. 14 (2001), pp. 246–255MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    A. Ageev and M. Sviridenko, An approximation algorithm for Hypergraph Max Cut with given sizes of parts, in Proceedings of European Simposium on Algorithms (ESA00).Google Scholar
  8. 8.
    S. Arora, P. Raghavan and S. Rao, Approximation schemes for Euclidean k- medians and related problems, STOC’ 98 (Dallas, TX), 106–113, ACM, New York, 1999.Google Scholar
  9. 9.
    V. Arya, N. Garg, R. Khandekar, V. Pandit, A. Meyerson and K. Munagala, Local Search Heuristics for k-median and Facility Location Problems, to appear in STOC01.Google Scholar
  10. 10.
    M. Charikar and S. Guha, Improved Combinatorial Algorithms for Facility Location and K-Median Problems, In Proceedings of IEEE Foundations of Computer Science, 1999.Google Scholar
  11. 11.
    M. Charikar, S. Khuller, G. Narasimhan and D. Mount, Facility Location with Outliers, in Proceedings of Symposium on Discrete Algorithms (SODA), (Jan 2001).Google Scholar
  12. 12.
    F. Chudak, Improved approximation algorithms for uncapacitated facility location, Integer programming and combinatorial optimization (Houston, TX, 1998), 180–194, Lecture Notes in Comput. Sci. 1412, Springer, Berlin, 1998.CrossRefGoogle Scholar
  13. 13.
    F. Chudak and D. Shmoys, Improved approximation algorithms for the capacitated facility location problem, In the Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (1999), 875–876.Google Scholar
  14. 14.
    F. Chudak and D. Shmoys, Improved approximation algorithms for uncapacitated facility location, manuscript.Google Scholar
  15. 15.
    F. Chudak nad D. Williamson, Improved approximation algorithms for capacitated facility location problems, Integer programming and combinatorial optimization (Graz, 1999), 99–113, Lecture Notes in Comput. Sci., 1610, Springer, Berlin, 1999.CrossRefGoogle Scholar
  16. 16.
    G. Cornuejols, M. L. Fisher and G. L. Nemhauser, Location of Bank Accounts to Optimize Float: An Analytic Study Exact and Approximate Algorithms, Management Science 23 (1977), 789–810.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    U. Feige, A Threshold of ln n for Approximating Set Cover, Journal of ACM 45 (1998), 634–652.MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    S. Guha and S. Khuller, Greedy strikes back: improved facility location algorithms, Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 1998), J. Algorithms 31 (1999), 228–248.MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    S. Guha, A. Meyerson and K. Munagala, Improved Algorithms for Fault Tolerant Facility Location, Proceedings of 12th ACM-SIAM Symposium on Discrete Algorithms, 2001.Google Scholar
  20. 20.
    G. Hardy, J. Littlewood and G. Pólya, Inequalities, Reprint of the 1952 edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1988.zbMATHGoogle Scholar
  21. 21.
    D. Hochbaum, Heuristics for the fixed cost median problem, Math. Programming 22 (1982), 148–162.MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    K. Jain, M. Mahdian and A. Saberi, A new greedy approach for facility location problems, to appear in STOC01.Google Scholar
  23. 23.
    K. Jain and V. Vazirani, Approximation Algorithms for Metric Facility Location and k-Median Problems Using the Primal-Dual Schema and Lagrangian Relaxation, Proc. 1999 FOCS, to appear in JACM.Google Scholar
  24. 24.
    S. Kolliopoulos and S. Rao, A nearly linear-time approximation scheme for the Euclidean k-median problem, Algorithms—ESA’ 99 (Prague), 378–389, Lecture Notes in Comput. Sci., 1643, Springer, Berlin, 1999.CrossRefGoogle Scholar
  25. 25.
    M. Korupolu, G. Plaxton, and R. Rajaraman, Analysis of a local search heuristic for facility location problems, Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 1998), J. Algorithms 37 (2000), 146–188.MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    J. Lin and J. Vitter, Approximation algorithms for geometric median problems, Inform. Process. Lett. 44 (1992), 245–249.MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    M. Mahdian, E. Markakis, A. Saberi and V. Vazirani, A greedy facility location algorithm ananlyzed using dual fitting, APPROX 2001, LNCS 2129, pp. 127–137.Google Scholar
  28. 28.
    M. Mahdian, Y. Ye, and J. Zhang, A 1.52-Approximation Algorithm for the Uncapacitated Facility Location Problem, manuscript, 2002.Google Scholar
  29. 29.
    R. Mettu and G. Plaxton, The online median problem, In Proceedings of FOCS00, 339–348.Google Scholar
  30. 30.
    A. Meyerson, K. Munagala and S. Plotkin, Web Caching using Access Statistics, in Proceedings of 12th ACM-SIAM Symposium on Discrete Algorithms, 2001.Google Scholar
  31. 31.
    P. Mirchandani and R. Francis, eds. Discrete location theory, Wiley-Interscience Series in Discrete Mathematics and Optimization. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1990.Google Scholar
  32. 32.
    D. Shmoys, E. Tardos and K. Aardal, Approximation algorithms for facility location problems, In 29th ACM Symposium on Theory of Computing (1997), 265–274.Google Scholar
  33. 33.
    N. Young, k-medians, facility location, and the Chernoff-Wald bound, Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 2000), 86–95, ACM, New York, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Maxim Sviridenko
    • 1
  1. 1.IBM T. J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations