On the k-layer planar subset and topological via minimization problems

Two closely related problems important for performance-driven layout design, the k-layer planar subset problem (k-PSP) and the k-layer topological via minimization problem, are studied. It is shown that both are NP-complete. Moreover, both problems can be solved in polynomial time when the routing regions are crossing channels. It can be shown that under a suitable assumption, all the channels for interblock connections in the general cell design style are crossing channels. The algorithms are based on an efficient algorithm for computing a maximum weighted k -cofamily in a partially ordered set