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This paper provides a novel approach for optimal route planning by making efficient use of the underlying geometrical structure. It combines classical artificial intelligence exploration with computational geometry. Given a set of global positioning system (GPS) trajectories, the input is refined by geometric filtering and rounding algorithms. For constructing the graph and the according point-localization structure, fast scan line and divide-and-conquer algorithms are applied. For speeding up the optimal online search algorithms, the geometrical structure of the inferred weighted graph is exploited in two ways; it is compressed while retaining the original information for unfolding resulting shortest paths and is then annotated by lower bounds and refined topographic information (for example, by the bounding boxes of all shortest paths that start with a given edge). Traffic disturbances can result in an increase in travel time for the affected area that, in turn, can affect the precomputed information. This paper discusses two models of introducing dynamics in a navigation system. The online planning system GPS-ROUTE implements the above techniques and provides a client-server web interface to answer a series of shortest-path or shortest-time queries.