Transit Node Routing Reconsidered

Transit Node Routing (TNR) is a fast and exact distance oracle for road networks. We show several new results for TNR. First, we give a surprisingly simple implementation fully based on Contraction Hierarchies that speeds up preprocessing by an order of magnitude approaching the time for just finding a CH (which alone has two orders of magnitude larger query time). We also develop a very effective purely graph theoretical locality filter without any compromise in query times. Finally, we show that a specialization to the online many-to-one (or one-to-many) shortest path further speeds up query time by an order of magnitude. This variant even has better query time than the fastest known previous methods which need much more space.Comment: 19 pages, submitted to SEA'201

UnLimited TRAnsfers for Multi-Modal Route Planning: An Efficient Solution

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

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

Computing distance tables is important for many logistics problems like the vehicle routing problem (VRP). While shortest distances from all source nodes in S to all target nodes in T are time-independent, travel times are not. We present the first efficient algorithms to compute time-dependent travel time tables in large time-dependent road networks. Our algorithms are based on time-dependent contraction hierarchies (TCH), currently the fastest time-dependent speed-up technique. The computation of a table is inherently in Theta(|S|*|T|), and therefore inefficient for large tables. We provide one particular algorithm using only Theta(|S|+|T|) time and space, being able to answer queries two orders of magnitude faster than the basic TCH implementation. If small errors are acceptable, approximate versions of our algorithms are further orders of magnitude faster

Robust Mobile Route Planning with Limited Connectivity

We study the problem of route planning on mobile devices. There are two current approaches to this problem. One option is to have all the routing data on the device, which can then compute routes by itself. This makes it hard to incorporate traffic updates, leading to suboptimal routes. An alternative approach outsources the route computation to a server, which then sends only the route to the device. The downside is that a user is lost when deviating from the proposed route in an area with limited connectivity. In this work, we present an approach that combines the best of both worlds. The server performs the route computation but, instead of sending only the route to the user, it sends a corridor that is robust against deviations. We define these corridors properly and show that their size can be theoretically bounded in road networks. We evaluate their quality experimentally in terms of size and robustness on a continental road network. Finally, we introduce several algorithms to compute corridors efficiently. Our experimental analysis shows that our corridors are small but very robust against deviations, and can be computed quickly on a standard server

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle