Clustering with diversity

TL;DR

This paper introduces a 2-approximation algorithm for the clustering with diversity problem, ensuring clusters have diverse colors and minimal maximum radius, with extensions for outliers, relevant to privacy-preserving data publication.

Contribution

It provides the first constant-factor approximation for clustering with diversity and establishes its optimality under P≠NP, including extensions for handling outliers.

Findings

2-approximation algorithm for clustering with diversity

Matching lower bound proving optimality unless P=NP

Extensions for outlier handling in privacy contexts

Abstract

We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a 2-approximation to this problem for any $\ell$ when the objective is to minimize the maximum radius of any cluster. We show that the approximation ratio is optimal unless $\mathbf{P=NP}$, by providing a matching lower bound. Several extensions to our algorithm have also been developed for handling outliers. This problem is mainly motivated by applications in privacy-preserving data publication.