  In data summarization we want to choose $k$ prototypes in order to summarize
a data set. We study a setting where the data set comprises several demographic
groups and we are restricted to choose $k_i$ prototypes belonging to group $i$.
A common approach to the problem without the fairness constraint is to optimize
a centroid-based clustering objective such as $k$-center. A natural extension
then is to incorporate the fairness constraint into the clustering problem.
Existing algorithms for doing so run in time super-quadratic in the size of the
data set, which is in contrast to the standard $k$-center problem being
approximable in linear time. In this paper, we resolve this gap by providing a
simple approximation algorithm for the $k$-center problem under the fairness
constraint with running time linear in the size of the data set and $k$. If the
number of demographic groups is small, the approximation guarantee of our
algorithm only incurs a constant-factor overhead.
