We study the problem of servicing a set of ride requests by dispatching a set of shared vehicles, which is faced by ridesharing companies such as Uber and Lyft. Solving this problem at a large scale might be crucial in the future for effectively using large fleets of autonomous vehicles. Since finding a solution for the entire set of requests that minimizes the total driving time is NP-complete, most practical approaches process the requests one by one. Each request is inserted into any vehicle's route such that the increase in driving time is minimized. Although this variant is solvable in polynomial time, it still takes considerable time in current implementations, even when inexact filtering heuristics are used. In this work, we present a novel algorithm for finding best insertions, based on (customizable) contraction hierarchies with local buckets. Our algorithm finds provably exact solutions, is still 30 times faster than a state-of-the-art algorithm currently used in industry and academia, and scales much better. When used within iterative transport simulations, our algorithm decreases the simulation time for largescale scenarios with many requests from days to hours.

Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable contraction hierarchies by systematically exploring the associated separator decomposition tree. Compared to previous bucket-based approaches, our algorithm requires much less target-dependent preprocessing effort. Moreover, we use our novel approach in two concrete applications. The first application are online k-closest point-of-interest queries, where the points of interest are only revealed at query time. We achieve query times of about 25 milliseconds on a continental road network, which is fast enough for interactive systems. The second application is travel demand generation. We show how to accelerate a recently introduced travel demand generator by a factor of more than 50 using our novel nearest-neighbor algorithm.

We incorporate turn restrictions and turn costs into the route planning algorithm customizable contraction hierarchies (CCH). There are two common ways to represent turn costs and restrictions. The edge-based model expands the network so that road segments become vertices and allowed turns become edges. The compact model keeps intersections as vertices, but associates a turn table with each vertex. Although CCH can be used as is on the edge-based model, the performance of preprocessing and customization is severely affected. While the expanded network is only three times larger, both preprocessing and customization time increase by up to an order of magnitude. In this work, we carefully engineer CCH to exploit different properties of the expanded graph. We reduce the increase in customization time from up to an order of magnitude to a factor of about 3. The increase in preprocessing time is reduced even further. Moreover, we present a CCH variant that works on the compact model, and show that it performs worse than the variant on the edge-based model. Surprisingly, the variant on the edge-based model even uses less space than the one on the compact model, although the compact model was developed to keep the space requirement low.

We study the problem of graph partitioning for evolving road networks. While the road network of the world is mostly stable, small updates happen on a relatively frequent basis, as can been observed with the OpenStreetMap project (http://www.openstreetmap.org). For various reasons, professional applications demand the graph partition to stay roughly the same over time, and that changes are limited to areas where graph updates occur. In this work, we define the problem, present algorithms to satisfy the stability needs, and evaluate our techniques on continental-sized road networks. Besides the stability gains, we show that, when the changes are low and local, running our novel techniques is an order of magnitude faster than running graph partitioning from scratch.

We study a multi-modal route planning scenario consisting of a public transit network and a transfer graph representing a secondary transportation mode (e.g., walking or taxis). The objective is to compute all journeys that are Pareto-optimal with respect to arrival time and the number of required transfers. While various existing algorithms can efficiently compute optimal journeys in either a pure public transit network or a pure transfer graph, combining the two increases running times significantly. As a result, even walking between stops is typically limited by a maximal duration or distance, or by requiring the transfer graph to be transitively closed. To overcome these shortcomings, we propose a novel preprocessing technique called ULTRA (UnLimited TRAnsfers): Given a complete transfer graph (without any limitations, representing an arbitrary non-schedule-based mode of transportation), we compute a small number of transfer shortcuts that are provably sufficient for computing all Pareto-optimal journeys. We demonstrate the practicality of our approach by showing that these transfer shortcuts can be integrated into a variety of state-of-the-art public transit algorithms, establishing the ULTRA-Query algorithm family. Our extensive experimental evaluation shows that ULTRA is able to improve these algorithms from limited to unlimited transfers without sacrificing query speed, yielding the fastest known algorithms for multi-modal routing. This is true not just for walking, but also for other transfer modes such as cycling or driving.

Determining travel demand within a region of interest takes a considerable calibration effort, requiring transportation surveys, traffic counts, and empirical trip volumes. However, there is a need for demand calculation without substantial calibration, for example to generate large-scale benchmark data for evaluating transportation algorithms. In this work, we present several approaches for demand calculation that take as input only publicly available data, such as population and POI densities. Our algorithms build upon the recently proposed radiation model, which is inspired by job search models in economics. We show that a straightforward implementation of the radiation model does not scale to continental road networks, taking months even on a modern 16-core server. Therefore, we introduce more scalable implementations, substantially decreasing the running time by five orders of magnitude from months to seconds. An extensive experimental evaluation shows that the output of our algorithms is in accordance with demand data used in production systems. Compared to simple approaches previously used in algorithmic publications to generate benchmark data, our algorithms output demand data of better quality, take less time, and have similar implementation complexity.

Given an urban road network and a set of origin-destination (OD) pairs, the traffic assignment problem asks for the traffic flow on each road segment. A common solution employs a feasible-direction method, where the direction-finding step requires many shortest-path computations. In this paper, we significantly accelerate the computation of flow patterns, enabling interactive transportation and urban planning applications. We achieve this by revisiting and carefully engineering known speedup techniques for shortest paths, and combining them with customizable contraction hierarchies. In particular, our accelerated elimination tree search is more than an order of magnitude faster for local queries than the original algorithm, and our centralized search speeds up batched point-to-point shortest paths by a factor of up to 6. These optimizations are independent of traffic assignment and can be generally used for (batched) point-to-point queries. In contrast to prior work, our evaluation uses real-world data for all parts of the problem. On a metropolitan area encompassing more than 2.7 million inhabitants, we reduce the flow-pattern computation for a typical two-hour morning peak from 76.5 to 10.5 seconds on one core, and 4.3 seconds on four cores. This represents a speedup of 18 over the state of the art, and three orders of magnitude over the Dijkstra-based baseline.