Minimum Separation for Single-Layer Channel Routing

We provide a linear-time algorithm for determining the minimum separation required to route a channel when the connections can be realized in one layer. Differing from the usual “river-routing” context, we allow single-sided connections. The algorithm also works directly for problems with multiterminal nets and does not require wires to lie on an underlying grid, though it does use the rectilinear wiring model. The approach can also be used to obtain a routability test for single-layer switchboxes that corrects errors in the literature and is simpler than other correct approaches. These problems are of interest because they may arise as subtasks in routing problems involving more than one layer.