Title: Fair k-Center Clustering for Data Summarization,
Abstract: 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 objective.
Existing algorithms for doing so run in time super-quadratic in the size of the
data set. This is in contrast to the standard k-center objective that can be
approximately optimized 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. We demonstrate the
applicability of our algorithm on both synthetic and real data sets.