New algorithms for k-center and extensions

The problem of interest is covering a given point set with homothetic copies of several convex containers C(1) ,.., C(k), while the objective is to minimize the maximum over the dilatation factors. Such k-containment problems arise in various applications, e.g. in facility location, shape fitting, data classification or clustering. So far most attention has been paid to the special case of the Euclidean k-center problem, where all containers C(i) are Euclidean unit balls. New developments based on so-called core-sets enable not only better theoretical bounds in the running time of approximation algorithms but also improvements in practically solvable input. sizes. Here, we present some new geometric inequalities and a Mixed-Integer-Convex-Programming formulation. Both are used in a very effective branch-and-bound routine which not only improves on best. known running times in the Euclidean case but also handles general and even different containers among the Ci.