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Strategyproof Facility Location with Limited Locations

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Abstract

We study the mechanism design of facility location problems. The problem is to design mechanisms to select a set of locations on which to build a set of facilities, aiming to optimize some system objective and achieve desirable properties based on the strategic agents’ locations. The agents might have incentives to misreport their private locations, in order to minimize the costs (i.e., the distance from the closest facility). We study the setting with limited locations, that is, the facilities can only be built on a given finite set of candidate locations, rather than the whole space. For locating a single facility and two facilities on a real line, we propose strategyproof mechanisms with tight approximation ratios, under the objectives of minimizing the total cost and the maximum cost. Further, we consider the problem of locating an obnoxious facility from which the agents want to stay as far away as possible, and derive tight bounds on the approximation ratio of strategyproof mechanisms.

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Acknowledgements

The authors thank Min-Ming Li for the invaluable suggestions and comments.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Zhong-Zheng Tang

  2. Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai, 519087, Guangdong, China

    Chen-Hao Wang

  3. BNU-HKBU United International College, Zhuhai, 519087, Guangdong, China

    Chen-Hao Wang

  4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Meng-Qi Zhang

  5. University of Chinese Academy of Sciences, Beijing, 100049, China

    Meng-Qi Zhang

  6. Caritas Institute of Higher Education, Hong Kong, 999077, China

    Ying-Chao Zhao

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  1. Zhong-Zheng Tang
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  2. Chen-Hao Wang
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Corresponding author

Correspondence to Chen-Hao Wang.

Additional information

An extended abstract of this work appeared in the Proceedings of the 14th International Conference on Combinatorial Optimization and Applications (COCOA), 2020 [1]The work of Zhong-Zheng Tang was supported by the National Natural Science Foundation of China (No. 12101069) and Innovation Foundation of BUPT for Youth (No. 500421358). The work of Ying-Chao Zhao was partially supported by the Research Grants Council of the HKSAR, China (No. UGC/FDS11/E03/21)

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Tang, ZZ., Wang, CH., Zhang, MQ. et al. Strategyproof Facility Location with Limited Locations. J. Oper. Res. Soc. China 11, 553–567 (2023). https://doi.org/10.1007/s40305-021-00378-1

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  • DOI: https://doi.org/10.1007/s40305-021-00378-1

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