A density-based greedy router

A track-by-track routing algorithm based on a greedy heuristic on density structure is presented. By applying a dynamic programming technique using an accurate criterion of density structure, the algorithm guarantees finding a set of wire segments for a track whose routing can decrease the channel density by one, if it exists. It is believed that none of the existing track-by-track routers can achieve this even by resorting to exhaustive search. With its accurate calculation in selecting wire segments in each track, the new two-layer router solves Deutsch´s difficult example in 19 tracks in the two-layer restricted-Manhattan model by a simple density-related function, and the extended three-, four-, and five-layer routers also outperform other routers without backtracking, rerouting, or routing transformation. The experimental results are presented for performance comparison