  We study the problem of fairness in k-centers clustering on data with
disjoint demographic groups. Specifically, this work proposes a variant of
fairness which restricts each group's number of centers with both a lower bound
(minority-protection) and an upper bound (restricted-domination), and provides
both an offline and one-pass streaming algorithm for the problem. In the
special case where the lower bound and the upper bound is the same, our offline
algorithm preserves the same time complexity and approximation factor with the
previous state-of-the-art. Furthermore, our one-pass streaming algorithm
improves on approximation factor, running time and space complexity in this
special case compared to previous works. Specifically, the approximation factor
of our algorithm is 13 compared to the previous 17-approximation algorithm, and
the previous algorithms' time complexities have dependence on the metric
space's aspect ratio, which can be arbitrarily large, whereas our algorithm's
running time does not depend on the aspect ratio.
