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In this work, we study diversity-aware clustering problems where the datapoints are associated with multiple attributes resulting in intersectinggroups. A clustering solution need to ensure that a minimum number of clustercenters are chosen from each group while simultaneously minimizing theclustering objective, which can be either $k$-median, $k$-means or$k$-supplier. We present parameterized approximation algorithms withapproximation ratios $1+ \frac{2}{e}$, $1+\frac{8}{e}$ and $3$ fordiversity-aware $k$-median, diversity-aware $k$-means and diversity-aware$k$-supplier, respectively. The approximation ratios are tight assuming Gap-ETHand FPT $\neq$ W[2]. For fair $k$-median and fair $k$-means with disjointfaicility groups, we present parameterized approximation algorithm withapproximation ratios $1+\frac{2}{e}$ and $1+\frac{8}{e}$, respectively. Forfair $k$-supplier with disjoint facility groups, we present a polynomial-timeapproximation algorithm with factor $3$, improving the previous best knownapproximation ratio of factor $5$.

Diversity-aware clustering: Computational Complexity and Approximation Algorithms