Covering and piercing disks with two centers

Authors:
Hee-Kap Ahn;Sang-Sub Kim;Christian Knauer;Lena Schlipf;Chan-Su Shin;Antoine Vigneron
Affiliations:
Department of Computer Science and Engineering, POSTECH, Pohang, Korea;Department of Computer Science and Engineering, POSTECH, Pohang, Korea;Institute of Computer Science, Universität Bayreuth, Bayreuth, Germany;Institute of Computer Science, Freie Universität Berlin, Germany;Department of Digital and Information Engineering, Hankuk University of Foreign Studies, Yongin, Korea;Geometric Modeling and Scientific Visualization Center, KAUST, Thuwal, Saudi Arabia
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

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Abstract

We consider new versions of the two-center problem where the input consists of a set $\mathcal{D}$ of disks in the plane. We first study the problem of finding two smallest congruent disks such that each disk in $\mathcal{D}$ intersects one of these two disks. Then we study the problem of covering the set $\mathcal{D}$ by two smallest congruent disks. We give exact and approximation algorithms for these versions.