TY - JOUR
A1 - Atienza, Nieves
A1 - de Castro, Natalia
A1 - Cortés, Carmen
A1 - Garrido, M. Ángeles
A1 - Grima, Clara I.
A1 - Hernández, Gregorio
A1 - Márquez, Alberto
A1 - Moreno-González, Auxiliadora
A1 - Nöllenburg, Martin
A1 - Portillo, José Ramón
A1 - Reyes, Pedro
A1 - Valenzuela, Jesús
A1 - Trinidad Villar, Maria
A1 - Wolff, Alexander
T1 - Cover contact graphs
N2 - 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.
KW - Informatik
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-78845
ER -