An approach is provided for generating a minimum overlapping alternative path. The approach involves receiving a constraint parameter for traversing a path between a first location and a second location. The approach also involves determining a critical portion of the path that is to be traveled to satisfy the constraint parameter, and designating a remaining portion of the path that is not the critical portion as a non-critical portion. The approach further involves calculating one or more candidate minimum overlapping alternative paths for the non-critical portion of the path. The approach further involves generating the minimum overlapping alternative path between the first location and the second location by combining the critical portion of the path with a selected one of the one or more candidate minimum overlapping alternative paths that satisfies the constraint parameter.