A new approach to three- or four-layer channel routing

An approach to the three-layer or four-layer channel-routing problem is presented. A general technique that transforms a two-layer routing solution systematically into a three-layer routing solution is developed. The proposed router performs well in comparison with other three-layer channel routers proposed thus far. In particular, it provides a ten-track optimal solution for the famous Deutsch´s difficult example, whereas other well-known three-layer channel routers required 11 or more tracks. The approach is extended to four-layer channel routing. Given any two-layer channel-routing solution without an unrestricted dogleg that uses w tracks, the router can obtain a four-layer routing solution using no more than w/2 tracks. A theoretical upper bound d/2+2 for arbitrary four-layer channel routing problems is also given