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Cover contact graphs

Please always quote using this URN: urn:nbn:de:bvb:20-opus-78845
  • 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 seedWe 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.show moreshow less

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Metadaten
Author: 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
URN:urn:nbn:de:bvb:20-opus-78845
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Informatik
Language:German
Year of Completion:2012
Source:In: Journal of Computational Geometry (2012) 3(1), 102-131; http://jocg.org/index.php/jocg/article/view/66
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
GND Keyword:Informatik
Release Date:2013/07/09
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung