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A Local Search Approximation Algorithm for a Squared Metric k-Facility Location Problem

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Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10627))

Abstract

In this paper, we introduce a squared metric k-facility location problem (SM-k-FLP) which is a generalization of the squared metric facility location problem (SMFLP) and k-facility location problem (k-FLP). In the SM-k-FLP, we are given a client set \(\mathcal {C}\) and a facility set \(\mathcal {F} \) from a metric space, a facility opening cost \(f_i \ge 0\) for each \( i \in \mathcal {F}\), and an integer k. The goal is to open a facility subset \(F \subseteq \mathcal {F}\) with \( |F| \le k\) and to connect each client to the nearest open facility such that the total cost (including facility opening cost and the sum of squares of distances) is minimized. Using local search and scaling techniques, we offer a constant approximation algorithm for the SM-k-FLP.

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Acknowledgements

The research of the first author is supported by Higher Educational Science and Technology Program of Shandong Province (No. J15LN22). The second author is supported by Natural Science Foundation of China (No. 11531014). The fourth author is supported by Natural Science Foundation of China (No. 61672323) and Natural Science Foundation of Shandong Province (ZR2016AM28). The fifth author is supported by Beijing Excellent Talents Funding (No. 2014000020124G046).

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, People’s Republic of China

    Dongmei Zhang

  2. Department of Information and Operations Research, College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Dachuan Xu, Yishui Wang & Zhenning Zhang

  3. School of Computer Science and Technology, Shandong University, Jinan, 250101, People’s Republic of China

    Peng Zhang

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  1. Dongmei Zhang
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  2. Dachuan Xu
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  3. Yishui Wang
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  4. Peng Zhang
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  5. Zhenning Zhang
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Corresponding author

Correspondence to Dachuan Xu .

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Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Zhang, D., Xu, D., Wang, Y., Zhang, P., Zhang, Z. (2017). A Local Search Approximation Algorithm for a Squared Metric k-Facility Location Problem. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10627. Springer, Cham. https://doi.org/10.1007/978-3-319-71150-8_11

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  • DOI: https://doi.org/10.1007/978-3-319-71150-8_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71149-2

  • Online ISBN: 978-3-319-71150-8

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