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An approximation algorithm for k-facility location problem with linear penalties using local search scheme

Author

Listed:
  • Yishui Wang

    (Beijing University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

  • Donglei Du

    (University of New Brunswick)

  • Chenchen Wu

    (Tianjin University of Technology)

Abstract

In this paper, we consider an extension of the classical facility location problem, namely k-facility location problem with linear penalties. In contrast to the classical facility location problem, this problem opens no more than k facilities and pays a penalty cost for any non-served client. We present a local search algorithm for this problem with a similar but more technical analysis due to the extra penalty cost, compared to that in Zhang (Theoretical Computer Science 384:126–135, 2007). We show that the approximation ratio of the local search algorithm is $$2 + 1/p + \sqrt{3+ 2/p+ 1/p^2} + \epsilon $$ 2 + 1 / p + 3 + 2 / p + 1 / p 2 + ϵ , where $$p \in {\mathbb {Z}}_+$$ p ∈ Z + is a parameter of the algorithm and $$\epsilon >0$$ ϵ > 0 is a positive number.

Suggested Citation

  • Yishui Wang & Dachuan Xu & Donglei Du & Chenchen Wu, 2018. "An approximation algorithm for k-facility location problem with linear penalties using local search scheme," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 264-279, July.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-016-0080-2
    DOI: 10.1007/s10878-016-0080-2
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    Cited by:

    1. 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.

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