@article{Capoyleas1991GeometricC,
title={Geometric Clusterings},
author={Vasilis Capoyleas and G{\"u}nter Rote and Gerhard J. Woeginger},
journal={J. Algorithms},
year={1991},
volume={12},
pages={341-356}
}

A k-clustering of a given set of points in the plane is a partition of the points into k subsets (“clusters”). For any fixed k, we can find a k-clustering which minimizes any monotone function of the diameters or the radii of the clusters in polynomial time. The algorithm is based on the fact that any two clusters in an optimal solution can be separated by a line. AMS 1980 mathematics subject classification (1985 revision): 68Q20, (62H30, 90B99, 52A37) CR categories and subject descriptors… CONTINUE READING

Partitioning points and graphs to minimize the maximum or the sum of diameters

C. Monma, S. Suri

in: Graph Theory, Combinatorics and Applications, Vol. 2, Proc. Sixth Quadrennial Int. Conf. Theory and Appl. of Graphs, Kalamazoo, Michigan, May 1988, ed. Y. Alavi et al.; Wiley • 1991