  For a set of points in $\mathbb{R}^d$, the Euclidean $k$-means problems
consists of finding $k$ centers such that the sum of distances squared from
each data point to its closest center is minimized. Coresets are one the main
tools developed recently to solve this problem in a big data context. They
allow to compress the initial dataset while preserving its structure: running
any algorithm on the coreset provides a guarantee almost equivalent to running
it on the full data.
  In this work, we study coresets in a fully-dynamic setting: points are added
and deleted with the goal to efficiently maintain a coreset with which a
k-means solution can be computed. Based on an algorithm from Henzinger and Kale
[ESA'20], we present an efficient and practical implementation of a fully
dynamic coreset algorithm, that improves the running time by up to a factor of
20 compared to our non-optimized implementation of the algorithm by Henzinger
and Kale, without sacrificing more than 7% on the quality of the k-means
solution.
