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

We present in this paper a new approach to the three or four layer channel routing problem. Since two layer channel routing has been well studied, there are several two layer routers which can produce optimal or near optimal solution for almost all the practical problems. We develop a general technique which transforms a two layer routing solution systematically into a three layer routing solution. The solution transformation approach is different from previous approaches for three layer and multi-layer channel routing. Our router performs well in comparison with other three layer channel routers proposed thus far. In particular, it provides a 10-track optimal solution for the famous Deutsch’s difficult example, whereas other well-known three layer channel routers required 11 or more tracks. We extend our approach to four layer channel routing. Given any two layer channel routing solution without unrestricted dogleg that uses w tracks, our router can provably obtain a four layer routing solution using no more than R w /2 H tracks. We also give a new theoretical upper bound R d /2 H + 2 for arbitrary four layer channel routing problems.