In recent years, highly effective hierarchical and goal-directed speedup techniques for routing in large road networks have been developed. This paper makes a systematic study of combinations of such techniques. These combinations turn out to give the best results in many scenarios, including graphs for unit disk graphs, grid networks, and time-expanded timetables. Besides these quantitative results, we obtain general insights for successful combinations.

Contraction hierarchies are a simple hierarchical routing technique that has proved extremely efficient for static road networks. We explain how to generalize them to networks with time-dependent edge weights. This is the first hierarchical speedup technique for timedependent routing that allows bidirectional query algorithms. For large realistic networks with considerable time-dependence (Germany, weekdays) our method outperforms previous techniques with respect to query time using comparable or lower preprocessing time. 1

Abstract. Up to now, research on speed-up techniques for DIJKSTRA’s algorithm focused on single-criteria scenarios. The goal was to find the quickest route within a transportation network. However, the quickest route is often not the best one. A user might be willing to accept slightly longer travel times if the cost of the journey is less. A common approach to cope with such a situation is to find Pareto-optimal (concerning other metrics than travel times) routes. Such routes have the property that each route is better than any other route with respect to at least one metric under consideration, e.g., travel costs or number of train changes. In this work, we study multi-criteria search in road networks. On the one hand, we focus on the problem of limiting the number of Pareto paths. On the other hand, we present a multi-criteria variant of our recent SHARC algorithm. 1

Abstract. We present an extension of the well-known time-expanded approach for timetable information. By remodeling unimportant stations, we are able to obtain faster query times with less space consumption than the original model. Moreover, we show that our extensions harmonize well with speed-up techniques whose adaption to timetable networks is more challenging than one might expect. 1

Abstract. Recent research on fast route planning algorithms focused either on road networks or on public transportation. However, on the long run, we are interested in planning routes in a multi-modal scenario: we start by car to reach the nearest train station, ride the train to the airport, fly to an airport near our destination and finally take a taxi. In other words, we need to incorporate public transportation into road networks. However, we do not want to switch the type of transportation too often. We end up in a label constrained variant of the shortest path problem. In this work, we present a first efficient solution to a restricted variant of this problem including experimental results for transportation networks with up to 125 Mio. edges. 1

During the last years, a wide range of huge networks has been made available to researchers. The discovery of natural groups, a task called graph clustering, in such datasets is a challenge arising in many applications such as the analysis of neural, social, and communication networks. We here present Orca, a new graph clustering algorithm, which operates locally and hierarchically contracts the input. In contrast to most existing graph clustering algorithms, which operate globally, Orca is able to cluster inputs with hundreds of millions of edges in less than 2.5 hours, identifying clusterings with measurably high quality. Our approach explicitly avoids maximizing any single index value such as modularity, but instead relies on simple and sound structural operations. We present and discuss the Orca algorithm and evaluate its performance with respect to both clustering quality and running time, compared to other graph clustering algorithms.

Accelerating the computation of quickest paths in road networks has been undergoing a rapid development during the last years. The breakthrough idea for handling road networks with tens of millions of nodes was the concept of shortcuts, i.e., additional arcs that represent long paths in the input. Very recently, this concept has been transferred to time-dependent road networks where travel times on arcs are given by functions. Unfortunately, the concept of shortcuts yields a high increase in space consumption for time-dependent road networks since the travel time functions assigned to the shortcuts may become quite complex. In this work, we present how the space overhead induced by time-dependent SHARC, a technique relying on shortcuts as well, can be reduced significantely. As a result, we are able to reduce the overhead stemming from SHARC by a factor of up to 11.5 for the price of a loss in query performance of a factor of 4. The methods we present allow a flexible trade-off between space consumption and query performance.

Abstract. In [2], we observed that SHARC benefits from adding shortcuts to the graph. In this preliminary work, we show that plain Arc-Flags [8] and reachbased routing [7] can be accelerated by simply adding additional shortcuts to the graph. It turns out that arc-flags can be accelerated by a factor of up to 4, while reachbased routing benefits by a reduction of the settled nodes of a factor of up to 5.5 and with respect to runtime by a factor of up to 1.6. 1

Abstract. We study the problem of finding good alternative routes in road networks. We look for routes that are substantially different from the shortest path, have small stretch, and are locally optimal. We formally define the problem of finding alternative routes with a single via vertex, develop efficient algorithms for it, and evaluate them experimentally. Our algorithms are efficient enough for practical use and compare favorably with previous methods in both speed and solution quality. 1

In the multi-modal route planning problem we are given multiple transportation networks (e. g., pedestrian, road, public transit) and ask for a best integrated journey between two points. The main challenge is that a seemingly optimal journey may have changes between networks that do not reflect the user’s modal preferences. In fact, quickly computing reasonable multimodal routes remains a challenging problem: Previous approaches either suffer from poor query performance or their available choices of modal preferences during query time is limited. In this work we focus on computing exact multi-modal journeys that can be restricted by specifying arbitrary modal sequences at query time. For example, a user can say whether he wants to only use public transit, or also prefers to use a taxi or walking at the beginning or end of the journey; or if he has no restrictions at all. By carefully adapting node contraction, a common ingredient to many speedup techniques on road networks, we are able to compute point-to-point queries on a continental network combined of cars, railroads and flights several orders of magnitude faster than Dijkstra’s algorithm. Thereby, we require little space overhead and obtain fast preprocessing times. 1