We investigate the fine-grained complexity of approximating the classical k-median / k-means clustering problems in general metric spaces. We show how to improve the approximation factors to (1+2/e+ε) and (1+8/e+ε) respectively, using algorithms that run in fixed-parameter time. Moreover, we show that we cannot do better in FPT time, modulo recent complexity-theoretic conjectures.
@article{arxiv.1904.12334,
title = {Tight FPT Approximations for $k$-Median and $k$-Means},
author = {Vincent Cohen-Addad and Anupam Gupta and Amit Kumar and Euiwoong Lee and Jason Li},
journal= {arXiv preprint arXiv:1904.12334},
year = {2019}
}