Topological routing path search algorithm with incremental routability test

This paper describes a topological routing path search algorithm embedded in our rubber-band-based autorouter for single-layer printed circuit boards. The algorithm searches for a topological path that is guaranteed to be transformable into a physical wire satisfying design rules. Topological path search algorithms used in existing autorouters verify design rules only locally and approximately. However, it is preferable to satisfy design rules exactly in the global routing phase, especially for routing a densely wired printed circuit board. We propose a method for incrementally verifying design rules during the topological routing path search and describe several improvements to the algorithm that reduce the overhead of the routability test and suppress combinatorial explosion. We also discuss the practical feasibility of the proposed algorithm on the basis of the results of experiments using several printed circuit boards.