  The sliding window model of computation captures scenarios in which data is
arriving continuously, but only the latest $w$ elements should be used for
analysis. The goal is to design algorithms that update the solution efficiently
with each arrival rather than recomputing it from scratch. In this work, we
focus on $k$-clustering problems such as $k$-means and $k$-median. In this
setting, we provide simple and practical algorithms that offer stronger
performance guarantees than previous results. Empirically, we show that our
methods store only a small fraction of the data, are orders of magnitude
faster, and find solutions with costs only slightly higher than those returned
by algorithms with access to the full dataset.
