Robert Geisberger

Exact Routing in Large Road Networks Using Contraction Hierarchies

Contraction hierarchies are a simple approach for fast routing in road networks. Our algorithm calculates exact shortest paths and handles road networks of whole continents. During a preprocessing step, we exploit the inherent hierarchical structure of road networks by adding shortcut edges. A subsequent modified bidirectional Dijkstra algorithm can then find a shortest path in a fraction of a millisecond, visiting only a few hundred nodes. This small search space makes it suitable to implement it on a mobile device. We present a mobile implementation that also handles changes in the road network, like traffic jams, and that allows instantaneous routing without noticeable delay for the user. Also, an algorithm to calculate large distance tables is currently the fastest if based on contraction hierarchies.

Fast routing in very large public transportation networks using transfer patterns

We show how to route on very large public transportation networks (up to half a billion arcs) with average query times of a few milliseconds. We take into account many realistic features like: traffic days, walking between stations, queries between geographic locations instead of a source and a target station, and multi-criteria cost functions. Our algorithm is based on two key observations: (1) many shortest paths share the same transfer pattern, i.e., the sequence of stations where a change of vehicle occurs; (2) direct connections without change of vehicle can be looked up quickly. We precompute the respective data; in practice, this can be done in time linear in the network size, at the expense of a small fraction of non-optimal results. We have accelerated public transportation routing on Google Maps with a system based on our ideas. We report experimental results for three data sets of various kinds and sizes.

Alternative route graphs in road networks

Every human likes choices. But todays fast route planning algorithms usually compute just a single route between source and target. There are beginnings to compute alternative routes, but there is a gap between the intuition of humans what makes a good alternative and mathematical definitions needed for grasping these concepts algorithmically. In this paper we make several steps towards closing this gap: Based on the concept of an alternative graph that can compactly encode many alternatives, we define and motivate several attributes quantifying the quality of the alternative graph. We show that it is already NP-hard to optimize a simple objective function combining two of these attributes and therefore turn to heuristics. The combination of the refined penalty based iterative shortest path routine and the previously proposed Plateau heuristics yields best results. A user study confirms these results.

Minimum time-dependent travel times with contraction hierarchies

Time-dependent road networks are represented as weighted graphs, where the weight of an edge depends on the time one passes through that edge. This way, we can model periodic congestions during rush hour and similar effects. In this work we deal with the special case where edge weights are time-dependent travel times. Namely, we consider two problems in this setting: Earliest arrival queries ask for a minimum travel time route for a start and a destination depending on a given departure time. Travel time profile queries ask for the travel time profile for a start, a destination, and an interval of possible departure times. For an instance representing the German road network, for example, we can answer earliest arrival queries in less than 1.5ms. For travel time profile queries, which are much harder to answer, we need less than 40ms if the interval of possible departure times has a width of 24 hours. For inexact travel time profiles with an allowed error of about 1% this even reduces to 3.2ms. The underlying hierarchical representations of the road network, which are variants of a time-dependent contraction hierarchy (TCH), need less than 1GiB of space and can be generated in about 30 minutes. As far as we know, TCHs are currently the only method being able to answer travel time profile queries efficiently. Altogether, with TCHs, web servers with massive request traffic are able to provide fast time-dependent earliest arrival route planning and computation of travel time profiles.

Fast Detour Computation for Ride Sharing

Ride sharing becomes more and more popular not least because internet services help matching offers and request. However, current systems use a rather simple-minded functionality allowing to search for the origin and destination city, sometimes enriched with radial search around the cities. We show that theses services can be substantially improved using innovative route planning algorithms. More concretely, we generalize previous static algorithms for many-to-many routing to a dynamic setting and develop an additional pruning strategy. With these measures it becomes possible to match each request to

Efficient routing in road networks with turn costs

n

Time-dependent contraction hierarchies and approximation

offers using

Contraction of timetable networks with realistic transfers

2n+1

Route planning with flexible edge restrictions

exact travel time computations in a large road network in a fraction of a microsecond per offer. For requests spread over Germany according to population density, we are able to reduce the number of failing entries substantially. We are able to find a reasonable match for more than 60% of the failing entries left by contemporary matching strategies. Additionally, we halve the average waste of resources in the matches found compared to radial search.

Engineering Time-Dependent Many-to-Many Shortest Paths Computation.

We present an efficient algorithm for shortest path computation in road networks with turn costs. Each junction is modeled as a node, and each road segment as an edge in a weighted graph. Turn costs are stored in tables that are assigned to nodes. By reusing turn cost tables for identical junctions, we improve the space efficiency. Preprocessing based on an augmented node contraction allows fast shortest path queries. Compared to an edge-based graph, we reduce preprocessing time by a factor of 3.4 and space by a factor of 2.4 without change in query time.