@article{AtienzadeCastroCortesetal.2012,
author = {Atienza, Nieves and de Castro, Natalia and Cort{\´e}s, Carmen and Garrido, M. {\´A}ngeles and Grima, Clara I. and Hern{\´a}ndez, Gregorio and M{\´a}rquez, Alberto and Moreno-Gonz{\´a}lez, Auxiliadora and N{\"o}llenburg, Martin and Portillo, Jos{\´e} Ram{\´o}n and Reyes, Pedro and Valenzuela, Jes{\´u}s and Trinidad Villar, Maria and Wolff, Alexander},
title = {Cover contact graphs},
url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-78845},
year = {2012},
abstract = {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.},
subject = {Informatik},
language = {de}
}