Engineering Oracles for Time-Dependent Road Networks

Abstract

We implement and experimentally evaluate landmarkbased 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 timedependent 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 (HORN). It is based on a hierarchy of landmarks, with a few "global" landmarks at the top level possessing travel-time 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.

Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks

“…TD-CRP queries depict a noticeable error and perform somewhat worse than KaTCH or CATCHUp queries. TD-S+9 depicts the smallest average error of all nonexact approaches (Kontogiannis et al [17] reported another CFLAT configuration with even smaller errors but significantly slower queries).…”

“…We only have separate numbers for KaTCH and CATCHUp. For CFLAT, Kontogiannis et al [17] reported that path retrieval takes up to a third of the total query time. Our experiments show a similar amount for KaTCH.…”

“…It may find suboptimal paths. Another approach is FLAT [16] and its extension CFLAT [17]. CFLAT features sublinear query running time after subquadratic preprocessing and guarantees on the approximation error.…”

Intriguingly Simple and Efficient Time-Dependent Routing in Road Networks

“…[6] did the same with MLD/CRP. Another technique is FLAT [24]. Here the idea is to precompute the solutions from a set of landmarks to every node and during the query phase to route all sufficiently long paths through a landmark.…”

“…We further assume that these functions are periodic, i.e., the time-horizon is one day and time wraps around at midnight. This modeling is not new and has been studied extensively [12,14,8,27,10,4,18,6,24]. One further assumes that a car that enters an edge earlier must leave the edge earlier than a car that entered at a later moment.…”