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An approximation algorithm for the k-level facility location problem with outliers

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Abstract

In this paper, we study the k-level facility location problem with outliers (k-LFLPWO), which is an extension of the well-known k-level facility location problem (k-LFLP). In the k-LFLPWO, we are given k facility location sets, a client location set of cardinality n and a non-negative integer \(q<n\). Every facility location set has a different level which belongs to \(\{1, 2,\ldots , k\}\). For any facility location, there is an opening cost. For any two locations, there is a connecting cost. We wish to connect at least \(n-q\) clients to opened facilities from level 1 to level k, such that the total cost including opening costs and connecting costs is minimized. Our main contribution is to present a 6-approximation algorithm, which is based on the technique of primal-dual, for the k-LFLPWO.

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Acknowledgements

The authors thank Yishui Wang for discussions of the k-LFLPWO and anonymous referees for their suggestions. The first author is supported by National Natural Science Foundation of China (Nos. 11871081, 12001523). The second author is supported by Beijing Natural Science Foundation Project (No. Z200002). The fourth author is supported by National Natural Science Foundation of China (No. 11971349).

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Authors and Affiliations

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

    Lu Han, Dachuan Xu & Dandan Liu

  2. College of Science, Tianjin University of Technology, Binshui Xidao, Xiqing District, Tianjin, 300384, People’s Republic of China

    Chenchen Wu

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  1. Lu Han
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  2. Dachuan Xu
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  3. Dandan Liu
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  4. Chenchen Wu
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Correspondence to Chenchen Wu.

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Han, L., Xu, D., Liu, D. et al. An approximation algorithm for the k-level facility location problem with outliers. Optim Lett 15, 2053–2065 (2021). https://doi.org/10.1007/s11590-021-01701-8

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