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

Geometric shortest path containers [online]

In this paper, we consider Dijkstra\u27s algorithm for the single source single target shortest path problem in large sparse graphs. The goal is to reduce the response time for on-line queries by using precomputed information. Due to the size of the graph, preprocessing space requirements can be only linear in the number of nodes. We assume that a layout of the graph is given. In the preprocessing, we determine from this layout a geometric object for each edge containing all nodes that can be reached by a shortest path starting with that edge. Based on these geometric objects, the search space for on-line computation can be reduced significantly. Shortest path queries can then be answered by Dijkstra\u27s algorithm restricted to edges where the corresponding geometric object contains the target. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are real-world traffic networks, the typical field of application for this scenario. Furthermore, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the geometric containers have to be updated. We evaluate the quality and the time for different update strategies that guarantee correct shortest paths. Finally, we present a software framework in C++ to realize the implementations of all of our variants of Dijkstra\u27s algorithm. A basic implementation of the algorithm is refined for each modification and - even more importantly - these modifications can be combined in any possible way without loss of efficiency

Dynamic Arc-Flags in Road Networks

International audienceIn this work we introduce a new data structure, named Road-Signs, which allows us to efficiently update the Arc-Flags of a graph in a dynamic scenario. Road-Signs can be used to compute Arc-Flags, can be efficiently updated and do not require large space consumption for many real-world graphs like, e.g., graphs arising from road networks. In detail, we define an algorithm to preprocess Road-Signs and an algorithm to update them each time that a weight increase operation occurs on an edge of the network. We also experimentally analyze the proposed algorithms in real-world road networks showing that they yields a significant speed-up in the updating phase of Arc-Flags, at the cost of a very small space and time overhead in the preprocessing phase

Edges as Nodes - a New Approach to Timetable Information

In this paper we suggest a new approach to timetable information by introducing the ``edge-converted graph'' of a timetable. Using this model we present simple algorithms that solve the earliest arrival problem (EAP) and the minimum number of transfers problem (MNTP). For constant-degree graphs this yields linear-time algorithms for EAP and MNTP which improves upon the known \emph{Dijkstra}-based approaches. We also test the performance of our algorithms against the classical algorithms for EAP and MNTP in the time-expanded model

Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT). BIT* uses a heuristic to efficiently search a series of increasingly dense implicit RGGs while reusing previous information. It can be viewed as an extension of incremental graph-search techniques, such as Lifelong Planning A* (LPA*), to continuous problem domains as well as a generalization of existing sampling-based optimal planners. It is shown that it is probabilistically complete and asymptotically optimal. We demonstrate the utility of BIT* on simulated random worlds in $\mathbb{R}^2$ and $\mathbb{R}^8$ and manipulation problems on CMU's HERB, a 14-DOF two-armed robot. On these problems, BIT* finds better solutions faster than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at http://www.youtube.com/watch?v=TQIoCC48gp