Abstract: A graph is selected for preprocessing. Partial shortest path trees are constructed for the vertices of the graph and shortcuts are added to the graph to reduce the reach of certain vertices. The partial trees can be used to divide the arcs into two groups, a high reach group and a low reach group wherein a reach threshold is used to divide the groups. This threshold may be a function of the number of iterations of the preprocessing algorithm performed thus far. Upper bounds on reach of the low reach arcs are computed, and these arcs are deleted from the graph. The preprocessing algorithm is applied iteratively to the remaining arcs in the graph, with the reach threshold changing based on the current iteration. At the end of the preprocessing phase all arc reaches are below the current threshold and are deleted. The graph obtained from the input graph by adding the shortcuts, together with the reach values, may then be used during a query phase to compute shortest paths between two vertices.

Abstract: Methods and systems are provided for computing shortest paths among a set of locations. A set of landmarks is dynamically selected by starting with two original landmarks and then improving the landmark selection based on distance to other landmarks. The landmarks are then used with A* search to find the shortest path from source to destination. Additional improvements are provided to reduce the amount of storage required. Landmarks may be generated or selected from a subset of landmarks during pre-processing using one or more selection heuristics, such as using tree-based heuristics and using a local search.