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New algorithms for k-center and extensions

  • René Brandenberg
  • Lucia Roth
Article

Abstract

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. 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-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 C i .

Keywords

Approximation algorithms Branch-and-bound Computational geometry Geometric inequalities Containment Core-sets k-center Diameter partition SOCP 2-SAT 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenGarching b. MünchenGermany

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