Diversity-aware clustering: Computational Complexity and Approximation Algorithms

Abstract

In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from each group should be within the range defined by a lower and upper bound threshold for each group, while simultaneously minimizing the clustering objective, which can be either $k$-median, $k$-means or $k$-supplier. We study the computational complexity of the proposed problems, offering insights into their NP-hardness, polynomial-time inapproximability, and fixed-parameter intractability. We present parameterized approximation algorithms with approximation ratios $1+ \frac{2}{e} + ε\approx 1.736$