Fair Range k-center

TL;DR

This paper introduces new algorithms for fair k-centers clustering that enforce demographic group constraints, improving approximation and efficiency especially in streaming settings.

Contribution

It proposes a novel fairness model with bounds on group centers and provides both offline and streaming algorithms with improved theoretical guarantees.

Findings

Offline algorithm matches previous time complexity and approximation in special case.

Streaming algorithm achieves better approximation factor of 13, improving over 17.

Running time of streaming algorithm is independent of metric space aspect ratio.

Abstract

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.