Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
Zhen Zhang, Xiaohong Chen, Limei Liu, Jie Chen, Junyu Huang, Qilong Feng
Fair-range clustering extends classical clustering formulations by associating each data point with one or more demographic labels. It imposes lower and upper bound constraints on the number of facilities opened for each label, ensuring fair representation of all demographic groups by the selected facilities. In this paper we focus on the fair-range $k$-median and $k$-means problems in Euclidean spaces. We give $(1+\varepsilon)$-approximation algorithms with fixed-parameter tractable running times for both problems, parameterized by the numbers of opened facilities and demographic labels. For Euclidean metrics, these are the first parameterized approximation schemes for the problems, improving upon the previously known $O(1)$-approximation ratios given by Thejaswi et al. (KDD 2022).