New Algorithms for k-Center and Extensions

The problem of interest is covering a given point set with homothetic copies of several convex containers C1,...,Ck, 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 Ci are Euclidean unit balls. Recent 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-ConvexProgramming 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. Keywords approximation algorit...

• Type: Conference
• Year: 2008
• Where: COCOA
• Authors: René Brandenberg, Lucia Roth
• Keywords: Approximation Algorithms, COCOA 2008, Discrete Geometry, Euclidean K-center Problem, Geometric Inequalities