Topological via minimization and routing

The authors consider topological via minimization (TVM) and topological routing (TR) of a two-point nets on two layers. They present a graph coloring technique for via minimization and also use it to derive bounds on the number of vias. The bounds are net intersection dependent. The complexity of coloring procedure is O(n²). The coloring procedure shows an abrupt drop in complexity, when intersection density is about 20%. For TR an O(n⁴) algorithm is presented which guarantees at most one via per net. Using the authors´ TVM and TR procedures, constraints such as assignment of nets to a particular layer, assignment of via to a particular net, and via density control can be implemented