Some embodiments of the invention provide a method for identifying topological
routes in a multi-layer region of a design layout. The method selects a first net
that has several routable elements. For the selected net, it then specifies a first
multi-layer topological route that connects the first net's routable elements before
selecting another net for routing. The first topological route traverses a plurality
of layers. In addition, a topological route is a route that represents a set of
diffeomorphic geometric routes.