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An improved approximation algorithm for uncapacitated facility location problem with penalties

Author

Listed:
  • Guang Xu

    (University at Buffalo, the State University of New York)

  • Jinhui Xu

    (University at Buffalo, the State University of New York)

Abstract

In this paper, we consider an interesting variant of the classical facility location problem called uncapacitated facility location problem with penalties (UFLWP for short) in which each client is either assigned to an opened facility or rejected by paying a penalty. The UFLWP problem has been effectively used to model the facility location problem with outliers. Three constant approximation algorithms have been obtained (Charikar et al. in Proceedings of the Symposium on Discrete Algorithms, pp. 642–651, 2001; Jain et al. in J. ACM 50(6):795–824, 2003; Xu and Xu in Inf. Process. Lett. 94(3):119–123, 2005), and the best known performance ratio is 2. The only known hardness result is a 1.463-inapproximability result inherited from the uncapacitated facility location problem (Guha and Khuller in J. Algorithms 31(1):228–248, 1999). In this paper, We present a 1.8526-approximation algorithm for the UFLWP problem. Our algorithm significantly reduces the gap between known performance ratio and the inapproximability result. Our algorithm first enhances the primal-dual method for the UFLWP problem (Charikar et al. in Proceedings of the Symposium on Discrete Algorithms, pp. 642–651, 2001) so that outliers can be recognized more efficiently, and then applies a local search heuristic (Charikar and Guha in Proceedings of the 39th IEEE Symposium on Foundations of Computer Science, pp. 378–388, 1999) to further reduce the cost for serving those non-rejected clients. Our algorithm is simple and can be easily implemented.

Suggested Citation

  • Guang Xu & Jinhui Xu, 2009. "An improved approximation algorithm for uncapacitated facility location problem with penalties," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 424-436, May.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:4:d:10.1007_s10878-007-9127-8
    DOI: 10.1007/s10878-007-9127-8
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    Citations

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    Cited by:

    1. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    2. Kuzbakov, Yerlan & Ljubić, Ivana, 2024. "New formulations for two location problems with interconnected facilities," European Journal of Operational Research, Elsevier, vol. 314(1), pages 51-65.
    3. Li Zhang & Jing Yuan & Zhizhen Xu & Qiaoliang Li, 2023. "A combinatorial approximation algorithm for k-level facility location problem with submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-19, August.
    4. Adam N. Elmachtoub & Retsef Levi, 2016. "Supply Chain Management with Online Customer Selection," Operations Research, INFORMS, vol. 64(2), pages 458-473, April.
    5. Yicheng Xu & Dachuan Xu & Donglei Du & Chenchen Wu, 2017. "Local search algorithm for universal facility location problem with linear penalties," Journal of Global Optimization, Springer, vol. 67(1), pages 367-378, January.

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