6699
2012
deu
article
1
2013-07-09
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Cover contact graphs
We study problems that arise in the context of covering certain geometric objects called seeds (e.g., points or disks) by a set of other geometric objects called cover (e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, respectively, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in three types of tasks, both in the general case and in the special case of seeds on a line: (a) deciding whether a given seed set has a connected CCG, (b) deciding whether a given graph has a realization as a CCG on a given seed set, and (c) bounding the sizes of certain classes of CCG’s. Concerning (a) we give efficient algorithms for the case that seeds are points and show that the problem becomes hard if seeds and covers are disks. Concerning (b) we show that this problem is hard even for point seeds and disk covers (given a fixed correspondence between graph vertices and seeds). Concerning (c) we obtain upper and lower bounds on the number of CCG’s for point seeds.
urn:nbn:de:bvb:20-opus-78845
7884
In: Journal of Computational Geometry (2012) 3(1), 102-131; http://jocg.org/index.php/jocg/article/view/66
Nieves Atienza
Natalia de Castro
Carmen Cortés
M. Ángeles Garrido
Clara I. Grima
Gregorio Hernández
Alberto Márquez
Auxiliadora Moreno-González
Martin Nöllenburg
José Ramón Portillo
Pedro Reyes
Jesús Valenzuela
Maria Trinidad Villar
Alexander Wolff
deu
swd
Informatik
Datenverarbeitung; Informatik
open_access
Institut für Informatik
Universität Würzburg
https://opus.bibliothek.uni-wuerzburg.de/files/6699/091_jocg_3_1.pdf