New Algorithms for k-Center and Extensions

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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...
René Brandenberg, Lucia Roth
Added 18 Oct 2010
Updated 18 Oct 2010
Type Conference
Year 2008
Authors René Brandenberg, Lucia Roth
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