  Center-based clustering is a fundamental primitive for data analysis and
becomes very challenging for large datasets. In this paper, we focus on the
popular $k$-median and $k$-means variants which, given a set $P$ of points from
a metric space and a parameter $k<|P|$, require to identify a set $S$ of $k$
centers minimizing, respectively, the sum of the distances and of the squared
distances of all points in $P$ from their closest centers. Our specific focus
is on general metric spaces, for which it is reasonable to require that the
centers belong to the input set (i.e., $S \subseteq P$). We present
coreset-based 3-round distributed approximation algorithms for the above
problems using the MapReduce computational model. The algorithms are rather
simple and obliviously adapt to the intrinsic complexity of the dataset,
captured by the doubling dimension $D$ of the metric space. Remarkably, the
algorithms attain approximation ratios that can be made arbitrarily close to
those achievable by the best known polynomial-time sequential approximations,
and they are very space efficient for small $D$, requiring local memory sizes
substantially sublinear in the input size. To the best of our knowledge, no
previous distributed approaches were able to attain similar quality-performance
guarantees in general metric spaces.
