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# Scalable Fair Clustering

*Proceedings of the 36th International Conference on Machine Learning*, PMLR 97:405-413, 2019.

#### Abstract

We study the fair variant of the classic k-median problem introduced by (Chierichetti et al., NeurIPS 2017) in which the points are colored, and the goal is to minimize the same average distance objective as in the standard $k$-median problem while ensuring that all clusters have an “approximately equal” number of points of each color. (Chierichetti et al., NeurIPS 2017) proposed a two-phase algorithm for fair $k$-clustering. In the first step, the pointset is partitioned into subsets called fairlets that satisfy the fairness requirement and approximately preserve the k-median objective. In the second step, fairlets are merged into k clusters by one of the existing k-median algorithms. The running time of this algorithm is dominated by the first step, which takes super-quadratic time. In this paper, we present a practical approximate fairlet decomposition algorithm that runs in nearly linear time.