Fully Dynamic Speed-Up Techniques for Multi-criteria Shortest Path Searches in Time-Dependent Networks

Abstract

We introduce two new speed-up techniques for time-dependent point-to-point shortest path problems with fully-dynamic updates in a multi-criteria setting. Our first technique, called SUBITO, is based on a specific substructure property of time-dependent paths which can be lower bounded by their minimal possible travel time. It requires no preprocessing, and the bounds can be computed on-the-fly for each query. We also introduce k-flags, an extension of arc flags, which assigns to each arc one of k levels for each region of a vertex partition. Intuitively, the higher the level of an arc for a certain destination, the larger the detour with respect to travel time. k-flags allow us to handle dynamic changes without additional time-consuming preprocessing.

In an extensive computational study using the train network of Germany we analyze these and other speed-up techniques with respect to their robustness under high and realistic update rates. We show that speed-up factors are conserved under different scenarios, namely a typical day of operation, distributed delays after “heavy snowfall”, and a major disruption at a single station. In our experiments, k-flags combined with SUBITO have led to the largest speed-up factors, but only marginally better than SUBITO alone. These observations can be explained by studying the distribution of k-flags. It turns out that only a small fraction of arcs can be excluded if one wants to guarantee exact Pareto-optimal point-to-point queries.

This work was partially supported by the DFG Focus Program Algorithm Engineering, grant Mu 1482/4-1. We wish to thank Deutsche Bahn AG for providing us timetable data for scientific use.