Published March 17, 2016
| Version v1
Publication
Cover contact graphs
Creators
- Atienza Martínez, María Nieves
- Castro Ochoa, Natalia de
- Cortés Parejo, María del Carmen
- Garrido Vizuete, María de los Angeles
- Grima Ruiz, Clara Isabel
- Hernández, Gregorio
- Márquez Pérez, Alberto
- Moreno González, Auxiliadora
- Nöllenburg, Martin
- Portillo Fernández, José Ramón
- Reyes Colume, Pedro
- Valenzuela Muñoz, Jesús
- Villar Liñán, María Trinidad
- Wolff, Alexander
Contributors
Description
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.
Additional details
Identifiers
- URL
- https://idus.us.es/handle/11441/38745
- URN
- urn:oai:idus.us.es:11441/38745
Origin repository
- Origin repository
- USE