On locally optimal breaking of complex cyclic vertical constraints in VLSI channel routing

Existing theory has supported deterministic polynomial time procedures for locally optimal breaking (LOB) of two classes of directed circuits (DC) in the vertical constraint graph, the classes of vertex disjoint DCs, and of couples of connected DCs. New LOB theory is reported that supports procedures for LOB of any number of DCs sharing a common vertex, or a common path, and of DCs in uniform ladder VCGs. A significant aspect of the new theory is that it relies on procedures for couples of connected DCs as tools for breaking more complex structures of connected DCs. Application of the theory in genetic channel routers is reported elsewhere.