One of commercial applications of mobile computing is ATIS(Advanced Traveler Information Systems) in ITS(Intelligent Transport Systems). In ATIS, a primary mobile computing task is to compute the shortest path from the current location to the destination. In this paper, we have studied the shortest path re-computation problem that arises in the DRGS(Dynamic Route Guidance System) in ATIS where the cost of topological digital road map is frequently updated as traffic condition changes dynamically. Previously suggested methods either re-compute the shortest path from scratch or re-compute the shortest path just between the two end nodes of the edge where the cost change occurs. However, these methods we trivial in that they do not intelligently utilize the previously computed shortest path information. In this paper, we propose an efficient approximate shortest path re-computation method based on the dynamic window scheme. The proposed method re-computes an approximate shortest path very quickly by utilizing the previously computed shortest path information. We first show the theoretical analysis of our methods and then present an in-depth experimental performance analysis by implementing it on grid graphs as well as a real digital road map.