For a path search that identifies a path between source and target states in a space, some embodiments of the invention provide a method for determining viability of an expansion of a path from a first state to a second dimensional state. The method computes a first cost function that expresses the cost of the path to reach the second state. The first cost function is defined over the second state. The method then determines whether the first cost function expresses a better cost over any portion of the second state than a second cost function that expresses the best cost of paths that have reached the second state during the path search. The expansion is a viable one if the first cost function expresses a better cost over at least a portion of the second state than the second cost function.