Approximating Fair k-Min-Sum-Radii in Euclidean Space

Lukas Drexler, Annika Hennes, Abhiruk Lahiri, Melanie Schmidt, Julian Wargalla

Abstract: The k-center problem is a classical clustering problem in which one is asked to find a partitioning of a point set P into k clusters such that the maximum radius of any cluster is minimized. It is well-studied. But what if we add up the radii of the clusters instead of only considering the cluster with maximum radius? This natural variant is called the k-min-sum-radii problem. It has become the subject of more and more interest in recent years, inspiring the development of approximation algorithms for the k-min-sum-radii problem in its plain version as well as in constrained settings.