A new approach to topological via minimization

A topological via minimization problem in a two-layer routing environment is examined. The problem of minimizing the number of vias needed to route n two-terminal nets in a bounded routing region is shown to be NP-hard. However, in the case of a two-shore routing region, the topological via minimization problem can be solved in O(n² log n) time. As a basis for the algorithm, a two-chain maximum dominance problem, which is of interest in its own right, is considered, and its applications to other very large-scale integration layout problems are shown