Sabine Storandt

Quick and energy-efficient routes: computing constrained shortest paths for electric vehicles

In this paper we study multi-criteria routing problems related to Electric Vehicles (EVs). Because EVs still suffer from a rather small cruising range restricted by the batterys capacity, and loading stations are sparse and reloading is time intensive, previous work focused on computing the most energy-efficient routes efficiently. Unfortunately these approaches do not guarantee anything in terms of distance or travel time. But even a very eco-friendly driver might not be willing to accept a tour three times as long as the quickest one to save some energy. Therefore we present new types of queries considering energy-consumption and distance or travel time and reloading effort, e.g. computing the shortest or quickest path on which the EV does not run out of energy while requiring at most k recharging events (with k being an input parameter). The respective optimization problems are instances of the constrained shortest path problem, which is NP-hard. Nevertheless we will provide preprocessing techniques that allow for fast query answering even in large street graphs.

On k-Path Covers and their applications

For a directed graph G with vertex set V we call a subset C ⊆ V a k-(All-)Path Cover if C contains a node from any path consisting of k nodes. This paper considers the problem of constructing small k-Path Covers in the context of road networks with millions of nodes and edges. In many application scenarios the set C and its induced overlay graph constitute a very compact synopsis of G which is the basis for the currently fastest data structure for personalized shortest path queries, visually pleasing overlays of subsampled paths, and efficient reporting, retrieval and aggregation of associated data in spatial network databases. Apart from a theoretical investigation of the problem, we provide efficient algorithms that produce very small k-Path Covers for large real-world road networks (with a posteriori guarantees via instance-based lower bounds).

Delay-Robustness of Transfer Patterns in Public Transportation Route Planning

Transfer pattern routing is a state-of-the-art speed-up technique for finding optimal paths which minimize multiple cost criteria in public transportation networks. It precomputes sequences of transfer stations along optimal paths. At query time, the optimal paths are searched among the stored transfer patterns, which allows for very fast response times even on very large networks. On the other hand, even a minor change to the timetables may affect many optimal paths, so that, in principle, a new computation of all optimal transfer patterns becomes necessary. In this paper, we examine the robustness of transfer pattern routing towards delay, which is the most common source of such updates. The intuition is that the deviating paths caused by typical updates are already covered by original transfer patterns. We perform experiments which show that the transfer patterns are remarkably robust even to large and many delays, which underlines the applicability and reliability of transfer pattern routing in realistic routing applications.

Real-time movement visualization of public transit data

We introduce a framework to create a world-wide live map of public transit, i.e. the real-time movement of all buses, subways, trains and ferries. Our system is based on freely available General Transit Feed Specification (GTFS) timetable data and also features real-time delay information (where available). The main problem of such a live tracker is the enormous amount of data that has to be handled (millions of vehicle movements). We present a highly efficient back-end that accepts temporal and spatial boundaries and returns all relevant trajectories and vehicles in a format that allows for easy rendering by the client. The real-time movement visualization of complete transit networks allows to observe the current state of the system, to estimate the transit coverage of certain areas, to display delays in a neat manner, and to inform a mobile user about near-by vehicles. Our system can be accessed via http://tracker.geops.ch/. The current implementation features over 80 transit networks, including the complete Netherlands (with real-time delay data), and various metropolitan areas in the US, Europe, Australia and New Zealand. We continuously integrate new data. Especially for Europe and North America we expect to achieve almost full coverage soon.

Frequency-based search for public transit

We consider the application of route planning in large public-transportation networks (buses, trains, subways, etc). Many connections in such networks are operated at periodic time intervals. When a set of connections has sufficient periodicity, it becomes more efficient to store the time range and frequency (e.g., every 15 minutes from 8:00am-6:00pm) instead of storing each of the time events separately. Identifying an optimal frequency-compression is NP-hard, so we present a time- and space-efficient heuristic. We show how we can use this compression to not only save space but also query time. We particularly consider profile queries, which ask for all optimal routes with departure times in a given interval (e.g., a whole day). In particular, we design a new version of Dijkstras algorithm that works with frequency-based labels and is suitable for profile queries. We evaluate the savings of our approach on two metropolitan and three country-wide public-transportation networks. On our largest network, we simultaneously achieve a better space consumption than all previous methods as well as profile query times that are about 5 times faster than the best previous method. We also improve Transfer Patterns, a state-of-the-art technique for fully realistic route planning in large public-transportation networks. In particular, we accelerate the expensive preprocessing by a factor of 60 compared to the original publication.

Contraction Hierarchies on Grid Graphs

Many speed-up techniques developed for accelerating the computation of shortest paths in road networks, like reach or contraction hierarchies, are based on the property that some streets are ’more important’ than others, e.g. on long routes the usage of an interstate is almost inevitable. In grids there is no obvious hierarchy among the edges, especially if the costs are uniform. Nevertheless we will show that contraction hierarchies can be applied to grid graphs as well. We will point out interesting connections to speed-up techniques shaped for routing on grids, like swamp hierarchies and jump points, and provide experimental results for game maps, mazes, random grids and rooms.

Result Diversity for Multi-Modal Route Planning

We study multi-modal route planning allowing arbitrary (meaningful) combinations of public transportation, walking, and taking a car / taxi. In the straightforward model, the number of Pareto-optimal solutions explodes. It turns out that many of them are similar to each other or unreasonable. We introduce a new filtering procedure, Types aNd Thresholds (TNT), which leads to a small yet representative subset of the reasonable paths. We consider metropolitan areas like New York, where a fast computation of the paths is difficult. To reduce the high computation times, optimality-preserving and heuristic approaches are introduced. We experimentally evaluate our approach with respect to result quality and query time. The experiments confirm that our result sets are indeed small (around 5 results per query) and representative (among the reasonable Pareto-optimal paths), and with average query times of about one second or less.

Path shapes: an alternative method for map matching and fully autonomous self-localization

We propose a novel scheme for map matching and fully autonomous self-localization. Our scheme is based on the unique characteristics of the shape of paths in a road network. As uniqueness of path shapes comes as no surprise in a world of infinite precision, we develop robust means of comparing shapes of paths under imprecisions. Even under this fuzzy comparison model, path shapes turn out to be sufficiently characteristic to allow for map matching or fully autonomous self-localization. We design an efficient data structure which allows for very fast path shape queries.

Personalized route planning in road networks

Computing shortest paths in road networks with millions of nodes and edges is challenging on its own. In the last few years, several preprocessing-based acceleration techniques have been developed to enable query answering orders of magnitudes faster than a plain Dijkstra computation. But most of these techniques work only if the metric which determines the optimal path is static or rarely changes. In contrast to that, we aim at answering personalized route planning queries. Here, every single query comes with a specification of its very own metric. This increases the combinatorial complexity of the problem significantly. We develop new preprocessing schemes that allow for real-time personalized route planning in huge road networks while keeping the memory footprint of the preprocessed data and subsequent queries small.

Scalable Transfer Patterns.

We consider the problem of Pareto-optimal route planning in public-transit networks of a whole country, a whole continent, or even the whole world. On such large networks, existing approaches suffer from either a very large space consumption, a very long preprocessing time or slow query processing. Transfer Patterns, a state-of-the-art technique for route planning in transit networks, achieves excellent query times, but the space consumption is large and the preprocessing time is huge. In this paper, we introduce a new scheme for the Transfer Pattern precomputation and query graph construction that reduces both the necessary preprocessing time and space consumption by an order of magnitude and more. Average query times are below 1 ms for local queries, independent of the size of the network, around 30 ms for non-local queries on the complete transit network of Germany, and an estimated 200 ms for a fictitious transit network covering the currently available data of the whole world.