Fair k-Center Clustering for Data Summarization

TL;DR

This paper introduces a linear-time approximation algorithm for fair k-center clustering, ensuring demographic fairness in data summarization without sacrificing computational efficiency.

Contribution

It presents the first linear-time approximation algorithm for fair k-center clustering, addressing the computational gap in existing methods.

Findings

Algorithm runs in linear time relative to data size and k

Approximation guarantee incurs only a constant-factor overhead for few groups

Effectively incorporates fairness constraints into clustering

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 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.