Geometric travel planning

This paper provides a novel approach for optimal route planning making efficient use of the underlying geometrical structure. It combines classical AI 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 on-line search algorithms, the geometrical structure of the inferred weighted graph is exploited in two ways. The graph is compressed while retaining the original information for unfolding resulting shortest paths. It is then annotated by lower bound refined topographic information; for example by the bounding boxes of all shortest paths that start with a given edge. The on-line planning system GPS-ROUTE implements the above techniques and provides a client-server Web interface to answer series of shortest-path or shortest-time queries.