On via minimization

Minimizing the number of vias in a two-layer circuit is known to reduce to a max cut problem in a planar graph. A similar reduction is presented that makes clear the planarity of the resulting graph. It is shown how to solve this problem in O(n/^3/2logn ) time, where n is the number of nodes of the graph. The first polynomial bound obtained for this problem was O(n³ ). Recently different authors also obtained an O(n^3/2logn) algorithm; however, they require a graph five times larger than the authors. Known results of polyhedral combinatorics are used to derive a min-max relation. If a heuristic is used, it is shown how to use linear programming duality to derive information about the quality of the heuristic solution