Abstract
In this paper, we study the mechanism design for two-facility-location games with the fractional preferences of agents, in which each agent has private information including her location in an interval [0, 1] and her fractional preference to indicate how much she prefers the two facilities. The decision maker needs to locate the two facilities to serve the agents, who has a utility equal to the interval length 1 minus the sum of weighted distances to both facilities. The facility locations are required to satisfy a minimum distance constraint, i.e., the distance of the two facilities must exceed a given number \(d\in [0,1]\). The goal is to design strategy-proof mechanisms to maximize the social/minimum utility among the agents. We propose a randomized strategy-proof mechanism, which is 2-approximation for both objectives of maximizing the social utility and minimum utility. We also propose a deterministic strategy-proof mechanism which has an approximation ratio of \(\frac{4}{2-d}\) and 4 for the two objectives, respectively. Furthermore, we derive corresponding lower bounds on the approximation ratios of strategy-proof mechanisms.
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Acknowledgement
Minming Li was partially supported by NSFC under Grant No. 11771365, and by Project No. CityU 11200518 from Research Grants Council of HKSAR.
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Duan, L., Gong, Z., Li, M., Wang, C., Wu, X. (2021). Mechanism Design for Facility Location with Fractional Preferences and Minimum Distance. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_42
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