Optimal wiring between rectangles

We consider the problem of wiring together two parallel rows of points under a variety of conditions. The options include whether we allow the rows to slide relative to one another, whether we use only rectilinear wires or arbitrary wires, and whether we can use wires in one layer or several layers. In almost all of these combinations of conditions, we can provide a polynomial-time algorithm to minimize the distance between the parallel rows of points. We also compare two fundamentally different wiring approaches, where one and two layers are used. We show that although the theoretical model implies that there can be great gains for the two-layer strategy, even in cases where no crossovers are required, when we consider typical design rules for laying out VLSI circuits there is no substantial advantage to the two-layer approach over the one-layer approach.