Zusammenfassung
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.