Necessary and sufficient conditions for the routability of classical channels

Abstract

This paper studies the solvability of the channel routing problem. Using a simple ‘constructive’ methodology, we prove which instances of the ‘classical’ channel routing problem can be solved. The set of non-solvable channels turns out to be remarkably small. Many existing channel routers, however, fail on channels which may be complicated, but which are now proven to be solvable. Although this result is mainly theoretical, the concepts and insights of the proof can be mapped directly into a very practical channel routing algorithm. This algorithm always finds a solution, whenever one exists. A multiple-layer gridless channel router was implementes using our concepts. It turned out to be very competitive, on benchmark channels as well as on real-life circuits.