Atienza, Nieves and Castro, Natalia de and Cortés, Carmen and Garrido, M. Ángeles and Grima, Clara I. and Hernández Peñalver, Gregorio and Márquez, Alberto and Moreno, Auxiliadora and Nöllenburg, Martin and Portillo, José Ramon and Reyes, Pedro and Valenzuela, Jesús and Villar, Maria Trinidad and Wolff, Alexander
Cover Contact Graphs..
In: "15th International Symposium on Graph Drawing, GD 2007", 23/09/2007-26/09/2007, Sydney, Australia. ISBN 978-3-540-77536-2.
We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pair wise disjoint, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in two types of tasks: (a) deciding whether a given seed set has a connected CCG, and (b) deciding whether a given graph has a realization as a CCG on a given seed set. Concerning task (a) we give efficient algorithms for the case that seeds are points and covers are disks or triangles. We show that the problem becomes NP-hard if seeds and covers are disks. Concerning task (b) we show that it is even NP-hard for point seeds and disk covers (given a fixed correspondence between vertices and seeds).