22 research outputs found
3-dimensional Channel Routing
Consider two parallel planar grids of size
w
×
n
. The vertices of these grids
are called terminals and pairwise disjoint subsets of termi
nals are called nets. We
aim at routing all nets in a cubic grid between the two layers h
olding the terminals.
However, to ensure solvability, it is allowed to introduce a
n empty row/column be-
tween every two consecutive rows/columns containing the te
rminals (in both grids).
Hence the routing is to be realized in a cubic grid of size 2
n
×
2
w
×
h
. The objective
is to minimize the height
h
. In this paper we generalize previous results of Recski
and Szeszl ́er [10] and show that every problem instance is so
lvable in polynomial
time with height
h
=
O
(max(
n, w
)). This linear bound is best possible (apart from
a constant factor)