Some embodiments of the invention provide a method for identifying a path in a design layout. Based on the design layout, the method defines a triangulated graph that has sets of source and target states and two orthogonal axes. The method specifies at least one path that starts from one state. It then iteratively specifies new paths by expanding previously specified paths in the graph until identifying a path that connects the source and target states. At least one of the expansions of a previously specified path is an expansion to a line that is not aligned with the axes of the graph.