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

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Abstract

We investigate k-level squared metric facility location problem with outliers (k-SMFLPWO) for any constant k. In k-SMFLPWO, given k facilities set \({\mathcal {F}}_{l}\), where \(l\in \{1, 2, \cdots , k\}\), clients set \({\mathcal {C}}\) with cardinality n and a non-negative integer \(q<n\). The sum of opening and connection cost will be substantially increased by distant clients. To minimize the total cost, some distant clients can not be connected, in short, at least \(n-q\) clients in clients set \({\mathcal {C}}\) are connected to the path \(p=(i_{1}\in {\mathcal {F}}_{1}, i_{2}\in {\mathcal {F}}_{2}, \cdots , i_{k}\in {\mathcal {F}}_{k})\) where the facilities in path p are opened. Based on primal-dual approximation algorithm and the property of squared metric triangle inequality, we present a constant factor approximation algorithm for k-SMFLPWO.

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Acknowledgements

We would like to thank two anonymous referees for their constructive comments. This work is supported by National Natural Science Foundation of China (No. 12071126).

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  1. School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Li Zhang, Jing Yuan & Qiaoliang Li

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  1. Li Zhang
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  2. Jing Yuan
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Correspondence to Qiaoliang Li.

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Zhang, L., Yuan, J. & Li, Q. An approximation algorithm for k-level squared metric facility location problem with outliers. Optim Lett 19, 139–149 (2025). https://doi.org/10.1007/s11590-024-02107-y

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