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A combinatorial approximation algorithm for k-level facility location problem with submodular penalties

Author

Listed:
  • Li Zhang

    (Hunan Normal University)

  • Jing Yuan

    (Hunan Normal University)

  • Zhizhen Xu

    (Hunan Normal University)

  • Qiaoliang Li

    (Hunan Normal University)

Abstract

We present an improved approximation algorithm for k-level facility location problem with submodular penalties, the new approximation ratio is 2.9444 for any constant k, which improves the current best approximation ratio 3.314. The central ideas in our results are as follows: first, we restructure the problem as an uncapacitated facility location problem, then we use the primal-dual scheme with greedy augmentation. The key technique of our result is that we change the way of last opening facility set in primal-dual approximation algorithm to get much more tight result for k-level facility location problem with submodular penalties.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:46:y:2023:i:1:d:10.1007_s10878-023-01067-w
    DOI: 10.1007/s10878-023-01067-w
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    References listed on IDEAS

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    1. 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.
    2. 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.
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