On the Complexity of Knock-Knee Channel Routing with 3-Terminal Nets
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).
Reference: R. A. Legenstein.
On the complexity of knock-knee channel routing with 3-terminal nets.
Technical Report, 2002.