Optimization and evaluation of shortest path queries

Levelwise Mesh Sparsification for Shortest Path Queries

The shortest path problem is one of the most fundamental problems in computer science. Although several quasi linear time algorithms have been proposed, even an optimal algorithm does not terminate in sufficiently short time for large-scale networks, such as web networks and road networks. An approach to solving this problem is to construct data structures that enable us to find solutions in a ...

Shortest path queries in rectilinear worlds

Highway Hierarchies Hasten Exact Shortest Path Queries

We present a new speedup technique for route planning that exploits the hierarchy inherent in real world road networks. Our algorithm preprocesses the eight digit number of nodes needed for maps of the USA or Western Europe in a few hours using linear space. Shortest (i.e. fastest) path queries then take around eight milliseconds to produce exact shortest paths. This is about 2 000 times faster...

Approximate Shortest Path Queries Using Voronoi Duals

We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows...

Ultrafast Shortest-Path Queries via Transit Nodes