Unconstrained multilayer switchbox routing

Consider the gradually more and more complex problems of single row routing, channel routing and switchbox routing on the one hand, and the gradually less and less restrictive models (1-layer, Manhattan, unconstrained 2-layer, multilayer) on the other hand. The single row routing problems can always be solved in the Manhattan model, and the channel routing problem can always be solved in the unconstrained 2-layer model, in fact, both in linear time. In this paper, the authors show that the switchbox routing problem is solvable in the multilayer model, also in linear time.