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In this paper, we study the problem of fair clustering on the $k-$centerobjective. In fair clustering, the input is $N$ points, each belonging to atleast one of $l$ protected groups, e.g. male, female, Asian, Hispanic. Theobjective is to cluster the $N$ points into $k$ clusters to minimize aclassical clustering objective function. However, there is an additionalconstraint that each cluster needs to be fair, under some notion of fairness.This ensures that no group is either "over-represented" or "under-represented"in any cluster. Our work builds on the work of Chierichetti et al. (NIPS 2017),Bera et al. (NeurIPS 2019), Ahmadian et al. (KDD 2019), and Bercea et al.(APPROX 2019). We obtain a randomized $3-$approximation algorithm for the$k-$center objective function, beating the previous state of the art($4-$approximation). We test our algorithm on real datasets, and show that ouralgorithm is effective in finding good clusters without over-representation orunder-representation, surpassing the current state of the art in runtime speed,clustering cost, while achieving similar fairness violations.

KFC: A Scalable Approximation Algorithm for $k$-center Fair Clustering