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On the Competitive Ratio for Online Facility Location

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

We consider the problem of Online Facility Location, where demands arrive online and must be irrevocably assigned to an open facility upon arrival. The objective is to minimize the sum of facility and assignment costs. We prove that the competitive ratio for Online Facility Location is Θ(log n/log log n). On the negative side, we show that no randomized algorithm can achieve a competitive ratio better than Ω(log n/log log n) against an oblivious adversary even if the demands lie on a line segment. On the positive side, we present a deterministic algorithm achieving a competitive ratio of O(log n/log log n). The analysis is based on a hierarchical decomposition of the optimal facility locations such that each component either is relatively well-separated or has a relatively large diameter, and a potential function argument which distinguishes between the two kinds of components.

This work was partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

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References

  1. S. Albers and H. Koga. New online algorithms for the page replication problem. J. of Algorithms, 27(1):75–96, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  2. B. Awerbuch, Y. Bartal, and A. Fiat. Competitive distributed file allocation. Proc. of STOC’ 93, pp. 164–173, 1993.

    Google Scholar 

  3. Y. Bartal. Probabilistic approximations of metric spaces and its algorithmic applications. Proc. of FOCS’ 96, pp. 184–193, 1996.

    Google Scholar 

  4. Y. Bartal, A. Fiat, and Y. Rabani. Competitive algorithms for distributed data management. J. of Computer and System Sciences, 51(3):341–358, 1995.

    Article  MathSciNet  Google Scholar 

  5. A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.

    Google Scholar 

  6. M. Charicar, C. Chekuri, T. Feder, and R. Motwani. Incremental clustering and dynamic information retrieval. Proc. of STOC’ 97, pages 626–635, 1997.

    Google Scholar 

  7. M. Charicar and R. Panigrahy. Clustering to minimize the sum of cluster diameters. Proc. of STOC’ 01, pages 1–10, 2001.

    Google Scholar 

  8. R. Fleischer and S. Seiden. New results for online page replication. Proc. of APPROX’ 00, LNCS 1913, pp. 144–154, 2000.

    Google Scholar 

  9. S. Guha. Approximation Algorithms for Facility Location Problems. PhD Thesis, Stanford University, 2000.

    Google Scholar 

  10. S. Guha and S. Khuller. Greedy strikes back: Improved facility location algorithms. Proc. of SODA’ 98, pp. 649–657, 1998.

    Google Scholar 

  11. M. Imase and B.M. Waxman. Dynamic Steiner tree problem. SIAM J. on Discrete Mathematics, 4(3):369–384, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  12. K. Jain and V. Vazirani. Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. J. of the ACM, 48(2):274–296, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  13. C. Lund, N. Reingold, J. Westbrook, and D.C.K. Yan. Competitive online algorithms for distributed data management. SIAM J. on Computing, 28(3):1086–1111, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Mahdian, Y. Ye, and J. Zhang. Improved approximation algorithms for metric facility location problems. Proc. of APPROX’ 02, LNCS 2462, pp. 229–242, 2002.

    Google Scholar 

  15. R.R. Mettu and C.G. Plaxton. The online median problem. Proc. of FOCS’ 00, pp. 339–348, 2000.

    Google Scholar 

  16. A. Meyerson. Online facility location. Proc. of FOCS’ 01, pp. 426–431, 2001.

    Google Scholar 

  17. D. Shmoys. Approximation algorithms for facility location problems. Proc. of APPROX’ 00, LNCS 1913, pp. 27–33, 2000.

    Google Scholar 

  18. D. Shmoys, E. Tardos, and K. Aardal. Approximation algorithms for facility location problems. Proc. of STOC’ 97, pp. 265–274, 1997.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Dimitris Fotakis

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  1. Dimitris Fotakis
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Fotakis, D. (2003). On the Competitive Ratio for Online Facility Location. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_51

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  • DOI: https://doi.org/10.1007/3-540-45061-0_51

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

  • eBook Packages: Springer Book Archive

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