Skip to main content
SpringerLink
Log in

A Greedy Facility Location Algorithm Analyzed Using Dual Fitting

  • Conference paper
  • First Online:
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques (RANDOM 2001, APPROX 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2129))

Abstract

We present a natural greedy algorithm for the metric uncapacitated facility location problem and use the method of dual fitting to analyze its approximation ratio, which turns out to be 1.861. The running time of our algorithm is O(m log m), where m is the total number of edges in the underlying complete bipartite graph between cities and facilities. We use our algorithm to improve recent results for some variants of the problem, such as the fault tolerant and outlier versions. In addition, we introduce a new variant which can be seen as a special case of the concave cost version of this problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Charikar and S. Guha. Improved combinatorial algorithms for facility location and k-median problems. Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, pp. 378–388, October 1999.

    Google Scholar 

  2. M. Charikar, S. Khuller, D. Mount, and G. Narasimhan. Algorithms for Facility Location Problems with Outliers. Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms, 2001.

    Google Scholar 

  3. F. Chudak and D. Shmoys. Improved approximation algorithms for the capacitated facility location problem. Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 875–876, 1999.

    Google Scholar 

  4. V. Chvatal. A greedy heuristic for the set covering problem. Math. Oper. Res. 4, pp. 233–235, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Guha and S. Khuller. Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, pp. 228–248, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Guha, A. Meyerson, and K. Munagala. Improved Approximation Algorithms for Fault-tolerant Facility Location. Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms, 2001.

    Google Scholar 

  7. D. S. Hochbaum. Heuristics for the fixed cost median problem. Math. Programming 22, 148–162, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  8. K. Jain, M. Mahdian, and A. Saberi. A new greedy approach for facility location problems, manuscript.

    Google Scholar 

  9. K. Jain and V. V. Vazirani. Primal-dual approximation algorithms for metric facility location and k-median problems. Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, pp. 2–13, October 1999.

    Google Scholar 

  10. K. Jain and V. Vazirani. An approximation algorithm for the fault tolerant metric facility location problem. Proceedings of APPROX 2000, pp. 177–183, 2000.

    MathSciNet  Google Scholar 

  11. M. R. Korupolu, C. G. Plaxton, and R. Rajaraman. Analysis of a local search heuristic for facility location problems. Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1–10, January 1998.

    Google Scholar 

  12. A. A. Kuehn and M. J. Hamburger. A heuristic program for locating warehouses. Management Science 9, pp. 643–666, 1963.

    Google Scholar 

  13. L. Lovasz. On the ratio of Optimal Integral and Fractional Covers. Discrete Math. 13, pp. 383–390, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Mettu and G. Plaxton. The online median problem. Proceedings of 41st IEEE FOCS, 2000.

    Google Scholar 

  15. S. Rajagopalan and V. V. Vazirani. Primal-dual RNC approximation of covering integer programs. SIAM J. Comput. 28, pp. 526–541, 1999.

    MathSciNet  Google Scholar 

  16. D. B. Shmoys, E. Tardos, and K. Aardal. Approximation algorithms for facility location problems. Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 265–274, May 1997.

    Google Scholar 

  17. M. Thorup. Quick k-median, k-center, and facility location for sparse graphs. To appear in ICALP 2001.

    Google Scholar 

  18. V. V. Vazirani. Approximation Algorithms, Springer-Verlag, Berlin, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, MIT, MA, 02139, USA

    Mohammad Mahdian

  2. Georgia Institute of Technology, College of Computing, GA, 30332, USA

    Evangelos Markakis, Amin Saberi & Vijay Vazirani

Authors
  1. Mohammad Mahdian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evangelos Markakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amin Saberi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vijay Vazirani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, MIT, Cambridge, MA, 02139, USA

    Michel Goemans

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, Université de Genéve, 24, Rue General Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  4. Computer Science Division, University of California at Berkeley, 615 Soda Hall, Berkeley, CA, 94720-1776, USA

    Luca Trevisan

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mahdian, M., Markakis, E., Saberi, A., Vazirani, V. (2001). A Greedy Facility Location Algorithm Analyzed Using Dual Fitting. In: Goemans, M., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. RANDOM APPROX 2001 2001. Lecture Notes in Computer Science, vol 2129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44666-4_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-44666-4_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42470-3

  • Online ISBN: 978-3-540-44666-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation