Abstract
Given a set of clients and a set of facilities with different priority levels in a metric space, the Budgeted Priority \(p\)-Median problem aims to open a subset of facilities and connect each client to an opened facility with the same or a higher priority level, such that the number of opened facilities associated with each priority level is no more than a given upper limit, and the sum of the client-connection costs is minimized. In this paper, we present a data reduction-based approach for limiting the solution search space of the Budgeted Priority p-Median problem, which yields a \((1+\varepsilon )\)-approximation algorithm running in \(O(nd\log n)+(p\varepsilon ^{-1})^{p\varepsilon ^{-O(1)}}n^{O(1)}\) time in d-dimensional Euclidean space, where \(n\) is the size of the input instance and p is the maximal number of opened facilities. The previous best approximation ratio for this problem obtained in the same time is \((3+\varepsilon )\).
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L. -M. Liu, X. -S. Xu, and Q. -L. Feng designed the study and contributed the central idea. Z. Zhang and Z.-Y. Huang did the analyses and wrote the initial draft of the paper. All authors discussed the results and revised the manuscript.
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This work was supported by the National Natural Science Foundation of China (Nos. 62202161, 62172446, and 62376092), Natural Science Foundation of Hunan Province (No. 2023JJ40240), and Open Project of Xiangjiang Laboratory (Nos.22XJ02002 and 22XJ03005).
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Zhang, Z., Huang, ZY., Tian, ZP. et al. On the Budgeted Priority p-Median Problem in High-Dimensional Euclidean Spaces. J. Oper. Res. Soc. China (2024). https://doi.org/10.1007/s40305-023-00533-w
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DOI: https://doi.org/10.1007/s40305-023-00533-w