Engineering Oracles for Time-Dependent Road Networks

We implement and experimentally evaluate landmark-based oracles for min-cost paths in two different types of road networks with time-dependent arc-cost functions, based on distinct real-world historic traffic data: the road network for the metropolitan area of Berlin, and the national road network of Germany. Our first contribution is a significant improvement on the implementation of the FLAT oracle, which was proposed and experimentally tested in previous works. Regarding the implementation, we exploit parallelism to reduce preprocessing time and real-time responsiveness to live-traffic reports. We also adopt a lossless compression scheme that severely reduces preprocessing space and time requirements. As for the experimentation, apart from employing the new data set of Germany, we also construct several refinements and hybrids of the most prominent landmark sets for the city of Berlin. A significant improvement to the speedup of FLAT is observed: For Berlin, the average query time can now be as small as 83μsec, achieving a speedup (against the time-dependent variant of Dijkstra’s algorithm) of more than 1, 119 in absolute running times and more than 1, 570 in Dijkstra-ranks, with worst-case observed stretch less than 0.781%. For Germany, our experimental findings are analogous: The average query-response time can be 1.269msec, achieving a speedup of more than 902 in absolute running times, and 1, 531 in Dijkstra-ranks, with worst-case stretch less than 1.534%. Our second contribution is the implementation and experimental evaluation of a novel hierarchical oracle (HORN). It is based on a hierarchy of landmarks, with a few “global” landmarks at the top level possessing traveltime information for all possible destinations, and many more “local” landmarks at lower levels possessing travel-time information only for a small neighborhood of destinations around them. As it was previously proved, the advantage of HORN over FLAT is that it achieves query times sublinear, not just in the size of the network, but in the Dijkstra-rank of the query at hand, while requiring asymptotically similar preprocessing space and time. Our experimentation of HORN in Berlin indeed demonstrates improvements in query times (more than 30.37%), Dijkstra-ranks (more than 39.66%), and also worst-case error (more than 35.89%), at the expense of a small blow-up in space. Finally, we implement and experimentally test a dynamic scheme to provide responsiveness to live-traffic reports of incidents with a small timelife (e.g., a temporary blockage of a road segment due to an accident). Our experiments also indicate that the traffic-related information can be updated in seconds.