Strategyproof Facility Location with Limited Locations

doi:10.1007/s40305-021-00378-1

Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (3): 553-567.doi: 10.1007/s40305-021-00378-1

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Strategyproof Facility Location with Limited Locations

Zhong-Zheng Tang¹, Chen-Hao Wang^2,3, Meng-Qi Zhang^4,5, Ying-Chao Zhao⁶

1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China;
2. Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai, 519087, Guangdong, China;
3. BNU-HKBU United International College, Zhuhai, 519087, Guangdong, China;
4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China;
5. University of Chinese Academy of Sciences, Beijing, 100049, China;
6. Caritas Institute of Higher Education, Hong Kong, 999077, China

Received:2021-03-15 Revised:2021-10-19 Online:2023-09-30 Published:2023-09-07
Contact: Chen-Hao Wang, Zhong-Zheng Tang, Meng-Qi Zhang, Ying-Chao Zhao E-mail:wangch@amss.ac.cn;tangzhongzheng@amss.ac.cn;mqzhang@amss.ac.cn;zhaoyingchao@gmail.com
Supported by:
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).

Abstract

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.

Key words: Mechanism design, Facility location, Social choice

CLC Number:

Zhong-Zheng Tang, Chen-Hao Wang, Meng-Qi Zhang, Ying-Chao Zhao. Strategyproof Facility Location with Limited Locations[J]. Journal of the Operations Research Society of China, 2023, 11(3): 553-567.

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Strategyproof Facility Location with Limited Locations

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