Some embodiments of the invention provide a method of searching for a three-dimensional global path between first and second sets of routable elements in a region of a layout that has multiple layers. The method partitions the region into several sub-regions. It then performs a path search to identify a path between a first set of sub-regions that contains the first-set elements and a second set of sub-regions that contain a second-set element. When the method performing the path search, it explores expansions along Manhattan and non-Manhattan routing directions between the sub-regions on a plurality of layers.