Some embodiments of the invention provide a method for identifying a path between a set of source states and a set of target states in a space with more than two dimensions. In some embodiments, the space includes a set of states and a transition map that specifies a set of states that can be reached from each particular state. At least some of the states are non-zero dimensional states. For instance, in some embodiments, the space is a graph that includes points, lines, and surfaces. The method specifies at least one path that starts from one state. It then iteratively specifies new paths by expanding previously specified paths to other states in the space until identifying a path that connects the source and target states. At least one of the expansions of a previously specified path includes an expansion in more than two dimensions of the space.