In this article we consider a basic problem in the layout of
VLSI-circuits, the channel-routing problem in the knock-knee mode.
We show that knock-knee channel routing with 3-terminal nets is
NP-complete and thereby settling a problem that was open for more
than a decade. In 1987, Sarrafzadeh showed that knock-knee channel
routing with 5-terminal nets is NP-complete.
Furthermore, it is known that this problem is solvable in polynomial
time if only 2-terminal nets are involved (This problem was
addressed for example by Frank in 1982 and by Formann, D. Wagner,
and F. Wagner in 1993).