Constrained via minimization for three-layer routing

The constrained via minimization problem for VLSI three-layer routing is the problem of determining which layers can be used for routing the wire segments in the interconnections of nets so that the number of vias is minimized. This problem has been shown to be NP-complete¹⁵. In this paper, this problem is first transformed to the contractibility problem of a three-colourable graph, then an heuristic algorithm is proposed on the basis of the graph contractability model. From experimental results, the algorithm proves faster and more efficient at generating very good results. For a typical case, the number of vias can be reduced by about 30%.