  Clustering is one of the most fundamental problems in unsupervised learning
with a large number of applications. However, classical clustering algorithms
assume that the data is static, thus failing to capture many real-world
applications where data is constantly changing and evolving. Driven by this, we
study the metric $k$-center clustering problem in the fully dynamic setting,
where the goal is to efficiently maintain a clustering while supporting an
intermixed sequence of insertions and deletions of points. This model also
supports queries of the form (1) report whether a given point is a center or
(2) determine the cluster a point is assigned to.
  We present a deterministic dynamic algorithm for the $k$-center clustering
problem that provably achieves a $(2+\epsilon)$-approximation in
poly-logarithmic update and query time, if the underlying metric has bounded
doubling dimension, its aspect ratio is bounded by a polynomial and $\epsilon$
is a constant. An important feature of our algorithm is that the update and
query times are independent of $k$. We confirm the practical relevance of this
feature via an extensive experimental study which shows that for values of $k$
and $\epsilon$ suggested by theory, our algorithmic construction outperforms
the state-of-the-art algorithm in terms of solution quality and running time.
