Local optimality theory in VLSI channel routing: composite cyclic vertical constraints

Local Optimality paradigm is applicable to all combinatorial optimization problems. Its direct field of application are the constructive solution algorithm; its main advantage is the low computational cost for multiple high quality initial solutions for iterative improvement algorithms. The application of the paradigm to the VLSI channel routing has necessitated the creation of new knowledge represented by the theory of locally optimal breaking (LOB) of directed circuits (DC) in the vertical constraint graph. Existing theory has supported deterministic polynomial time algorithms for LOB of two classes of directed circuits, the classes of vertex disjoint DCs, and of couples of connected DCs. The new LOB theory supports algorithms for more complex classes of any number of DCs sharing a single vertex and of a uniform lattices of DCs. It is significant that the new theory relies on the theory for couples of connected DCs for breaking more complex structures of connected DCs