Improved analysis of D2-sampling based PTAS for k-means and other Clustering problems

We give an improved analysis of the simple $D^2$-sampling based PTAS for the $k$-means clustering problem given by Jaiswal, Kumar, and Sen (Algorithmica, 2013). The improvement on the running time is from $O\left(nd \cdot 2^{\tilde{O}(k^2/ε)}\right)$ to $O\left(nd \cdot 2^{\tilde{O}(k/ε)}\right)$.

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