# Computing Largest Circles Separating Two Sets of Segments

1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : A circle $C$ separates two planar sets if it encloses one of the sets and its open interior disk does not meet the other set. A separating circle is a largest one if it cannot be locally increased while still separating the two given sets. An $\Theta(n \log n)$ optimal algorithm is proposed to find all largest circles separating two given sets of line segments when line segments are allow ed to meet only at their endpoints. This settles an open problem from a previous paper\cite{bcdy-csp-95}. In the general case, when line segments may intersect $Ømega(n^2)$ times, our algorithm can be adapted to work in $O(n \alpha(n) \log n)$ time and $O(n \alpha(n))$ space, where $\alpha(n)$ represents the extremely slowly growing inverse of Ackermann function.
Keywords :
Type de document :
Rapport
RR-2705, INRIA. 1995
Domaine :
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https://hal.inria.fr/inria-00073985
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 14:14:35
Dernière modification le : samedi 27 janvier 2018 - 01:31:29
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:20:48

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• HAL Id : inria-00073985, version 1

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Jean-Daniel Boissonnat, Jurek Czyzowicz, Olivier Devillers, Jorge Urrutia, Mariette Yvinec. Computing Largest Circles Separating Two Sets of Segments. RR-2705, INRIA. 1995. 〈inria-00073985〉

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