Cover Contact Graphs
Castro Ochoa, Natalia de
Cortés Parejo, María del Carmen
Garrido Vizuete, María de los Angeles
Grima Ruiz, Clara Isabel
Márquez Pérez, Alberto
Portillo Fernández, José Ramón
Reyes Colume, Pedro
Valenzuela Muñoz, Jesús
Villar Liñán, María Trinidad
|Department||Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)|
|Published in||Graph Drawing (2007), Lecture Notes in Computer Science, Vol. 4875 pp 171-182|
|Document type||Chapter of Book|
|Abstract||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 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 pairwise 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).