A high-speed shape-based router is applicable to standard-cell digital designs, chip-level-block assembly designs, and other styles of design. In a flow of the invention, the technique establishes an initial structure for each net to be routed. Nets or parts of them are ordered. Each part of the net may be routed using a spine routing search, depth first search, or a space flood search, or any combination of these. Where sections fail or an error occurs, conflicts are identified, and the technique tries routing again.