Skip to main content
SpringerLink
Log in

An approximation algorithm for the dynamic facility location problem with outliers

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this article, we investigate the dynamic (multi-period) facility location problem with potentially unserved clients or outliers. We propose a 3-approximation primal-dual algorithm based on an integer linear program formulation of the problem. We further improve the approximation ratio to 2 by combining the cost scaling and greedy improvement techniques.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Aardal, K., van den Berg, P.L., Gijswijt, D., Li, S.: Approximation algorithms for hard capacitated \(k\)-facility location problems. Eur. J. Oper. Res. 242(2), 358–368 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ageev, A., Ye, Y., Zhang, J.: Improved combinatorial approximation algorithm for the \(k\)-level facility location problem. SIAM J. Discrete Math. 18(1), 207–217 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Byrka, J., Rybicki, B., Uniyal, S.: An approximation algorithm for uniform capacitated \(k\)-median problem with \(1 + \epsilon \) capacity violation. In: Proceedings of the 18th Conference on Integer Programming and Combinatorial Optimization (2016)

  4. Chen, X., Chen, B.: Approximation algorithm for soft-capacitated facility location in capacitated network design. Algorithmica 53, 263–297 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Charikar M., Khuller S., Mount D.M., Narasimhan G.: Algorithms for facility location problems with outliers. In: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics. pp. 642–651 (2001)

  6. Charikar, M., Guha, S.: Improved combinatorial algorithms for the facility location. SIAM J. Comput. 34, 803–824 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chudak, F., Shmoys, D.: Improved approximation algorithm for the uncapacitated facility location problem. SIAM J. Comput. 33(1), 1–25 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Du, D., Lu, R., Xu, D.: A primal-dual approximation algorithm for the facility location problem with submodular penalties. Algorithmica 63, 191–200 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Guha, S., Khuller, S.: Greedy strikes back: improved facility location algorithms. J. Algorithms 31(1), 228–248 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hamilton M.M.: Loud and Clear, a Silent E. Washington Post. 23, (2000)

  11. Hochbaum, D.: Approximation Algorithms for NP-hard Problems. PWS Publishing Company, Boston (1997)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Kuehn, A., Hamburger, M.: A heuristic program for locating warehouses. Manag. Sci. 9, 643–666 (1963)

    Article  Google Scholar 

  14. Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. J. Algorithms 37(1), 146–188 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Li, S.: A \(1.488\)-approximation algorithm for the uncapacitated facility location problem. In: Proceedings of the 38th International Colloquim Conference on Automata, Languages and Programming, Part 2. pp. 77–88 (2011)

  16. Love, R., Morris, J., Wesolowsky, G.: Facilities Location: Models and Methods. North-Holland, New York (1988)

    MATH  Google Scholar 

  17. Mahdian, M., Ye, Y., Zhang, J.: Approximation algorithm for metric facility location problem. SIAM J. Comput. 36(2), 411–432 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mahdian, M., Ye, Y., Zhang, J.: Improved approximation algorithms for metric facility location problems. In: Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX), LNCS 2462, pp. 229–242. Springer-Verlag, New York (2002)

  19. Qiu, L., Padmanabhan, V., Voelker, G.: On the placement of web server replicas. In: Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 3, pp. 1587–1596 (2001)

  20. Sviridenko M.: Cited as personal communication in Chudak and Shmoys [7] (1998)

  21. Shmoys, D., Tardös, É., Aardal, K.: Approximation algorithm for facility location problems. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 265–274 (1997)

  22. Van Roy, T.J., Erlenkotter, D.: A dual-based procedure for dynamic facility location. Manag. Sci. 28(10), 1091–1105 (1982)

    Article  MATH  Google Scholar 

  23. Ye, Y., Zhang, J.: An approximation algorithm for the dynamic facility location problem. In: Cheng, M.X., Li, Y., Du, D-Z. (eds.) Combinatorial Optimization in Communication Networks, pp. 623–637. Springer, US (2006)

  24. Zhang, P.: A new approximation algorithm for the \(k\)-facility location problem. Theor. Comput. Sci. 384, 126–135 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The research of the second author is supported by NSFC (No. 11531014). The third author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 283106.

Author information

Authors and Affiliations

  1. Department of Information and Operations Research, College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, People’s Republic of China

    Yanjun Jiang & Dachuan Xu

  2. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

  3. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, People’s Republic of China

    Dongmei Zhang

Authors
  1. Yanjun Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dachuan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Donglei Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dongmei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dongmei Zhang.

Additional information

This paper has been presented in the 10th International Conference on Optimization Techniques and Applications (ICOTA 10).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, Y., Xu, D., Du, D. et al. An approximation algorithm for the dynamic facility location problem with outliers. Optim Lett 13, 561–571 (2019). https://doi.org/10.1007/s11590-017-1153-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-017-1153-6

Keywords

Search

Navigation