VLSI Routing in Polynomial Time

There are plenty of NP-complete problems in VLSI design, like channel routing or switchbox routing in the 2-layer Manhattan model. However, there are quite a few polynomially solvable problems as well, some of them (like the single row routing in the 2-layer Manhattan model) date back to the fifties. Here we survey some old and some more recent results (both polynomially solvable subcases and NP-completeness proofs) in a systematic way, taking into account two hierarchies, namely that of geometry (what to route) and technology (how to route) at the same time. Due to lack of space, this extended abstract does not contain references; a more detailed version is available from the author.