Tight FPT Approximations for k-Median and k-Means

04/28/2019

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by   Vincent Cohen-Addad, et al.

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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.