1 research outputs found
Recognizing Generalized Transmission Graphs of Line Segments and Circular Sectors
Suppose we have an arrangement of geometric objects in the plane, with a distinguished point
in each object . The generalized transmission graph of
has vertex set and a directed edge if and only
if . Generalized transmission graphs provide a generalized model
of the connectivity in networks of directional antennas.
The complexity class contains all problems that can be
reduced in polynomial time to an existential sentence of the form , where range over
and is a propositional formula with signature . The class aims to capture the complexity of
the existential theory of the reals. It lies between and
.
Many geometric decision problems, such as recognition of disk graphs and of
intersection graphs of lines, are complete for . Continuing
this line of research, we show that the recognition problem of generalized
transmission graphs of line segments and of circular sectors is hard for
. As far as we know, this constitutes the first such result
for a class of directed graphs.Comment: 11 pages, 5 figure