Via assignment problem in multilayer printed circuit board

In the routing of a multilayer printed circuit board an important phase is the via assignments. In this paper, the via assignment problem is given a graph theoretic formulation. Some related optimization problems are proven to belong to a particular class of hard combinatorial problem: the class of nondeterministic polynomial (NP)-complete problems. This result suggests that the only way to solve efficiently the optimization problems is to introduce heuristic algorithms. Hence, some heuristic algorithms a proposed and their performances are evaluated.