Engineering and Augmenting Route Planning Algorithms

Algorithm engineering exhibited an impressive surge of interest during the last years, spearheaded by one of the showpieces of algorithm engineering: computation of shortest paths. In principle, Dijkstra’s classical algorithm can solve this problem. However, for continental-sized transportation networks, Dijkstra’s algorithm would take up to 10 seconds for finding a suitable connection, which is way too slow for practical applications. Hence, many speed-up techniques have been developed during the last years with the fastest ones yielding query times of few microseconds on road networks. However, most developed techniques require the network to be static or only allow a small number of updates. In practice, however, travel duration often depends on the departure time. It turns out that efficient models for routing in almost all transportation systems, e.g., timetable information for railways or scheduling for airplanes, are based on time-dependent networks. Moreover, road networks are not static either: there is a growing body of data on travel times of important road segments stemming from roadside sensors, GPS systems inside cars, traffic simulations, etc. Using this data, we can assign speed profiles to roads. This yields a time-dependent road network. Switching from a static to a time-dependent scenario is more challenging than one might expect: The input size increases drastically as travel times on congested motorways change during the day. On the technical side, most static techniques rely on bidirectional search, i.e., a second search is started from the target. This concept is complicated in timedependent scenarios since the arrival time would have to be known in advance for such an approach. Moreover, possible problem statements for shortest paths become even more complex in such networks. A user could ask at what time she should depart in order to spend as little time traveling as possible. As a result, none of the existing high-performance techniques can be adapted to this realistic scenario easily. Furthermore, the fastest route in transportation networks is often not the “best” one. For example, users traveling by train may be willing to accept longer travel times if the number of required transfers is lower or the cost of a journey with longer duration is cheaper. We end up in a multi-criteria scenario in which none of the high-performance approaches developed in the last years can be applied easily. In this work, we introduce the first efficient, provably correct, algorithms for route planning in these augmented scenarios. Therefore, we follow the concept of algorithm engineering by designing, analyzing, implementing, and evaluating speed-up techniques for Dijkstra’s algorithm. For an augmentation, we additionally pursue a very systematic approach. First we identify basic concepts for accelerating shortest path queries and analyze their drawbacks. By adding a hierarchical component, i.e., contraction, we are able to remedy those drawbacks and derive speed-up techniques with similar performance in time-independent networks as existing approaches. However, due to their foundation on basic concepts, their augmentations are easier than for existing approaches.