Route Planning in Road Networks

Computing optimal routes in road networks is one of the showpieces of realworld applications of algorithmics. In principle, we could use Dijkstra’s algorithm—the ‘classic’ solution from graph theory. But for large road networks this would be far too slow. Therefore, there is considerable interest in speedup techniques, which typically invest some time into a preprocessing step in order to generate auxiliary data that can be used to accelerate all subsequent route planning queries. Following the paradigm of algorithm engineering, we design, implement, and evaluate three highly-efficient and provably accurate point-topoint route planning algorithms—all of which with different benefits—and one generic many-to-many approach, which computes for given node sets S and T the optimal distances between all node pairs (s, t) ∈ S × T in a very efficient way. The evaluation is done in an extensive experimental study using large real-world road networks with up to 33 726 989 junctions. Highway hierarchies exploit the inherent hierarchical structure of road networks and classify roads by importance. A point-to-point query is then performed in a bidirectional fashion—forwards from the source and backwards from the target—, disregarding more and more less important streets with increasing distance from source or target. Highway-node routing is a related bidirectional and hierarchical approach. Its conceptual simplicity and fast preprocessing allows the implementation of update routines that are able to react efficiently to unexpected events like traffic jams. Transit-node routing provides extremely fast query times by reducing most requests to a few table lookups, exploiting the observation that when driving to somewhere ‘far away’, the current location is always left via one of only a few ‘important’ traffic junctions. Our generic many-to-many algorithm can be instantiated based on certain bidirectional route planning techniques, for example, highway hierarchies or highway-node routing. It computes a complete |S| × |T | distance table, basically performing only |S| forward plus |T | backward queries instead of |S| times |T | bidirectional queries. Among all route planning methods that achieve considerable speedups, we currently provide the one with the fastest query times, the one with the fastest preprocessing, and the one with the lowest memory requirements.