Dynamic Time-Dependent Route Planning in Road Networks with User Preferences

There has been tremendous progress in algorithmic methods for computing driving directions on road networks. Most of that work focuses on time-independent route planning, where it is assumed that the cost on each arc is constant per query. In practice, the current traffic situation significantly influences the travel time on large parts of the road network, and it changes over the day. One can distinguish between traffic congestion that can be predicted using historical traffic data, and congestion due to unpredictable events, e.g., accidents. In this work, we study the \emph{dynamic and time-dependent} route planning problem, which takes both prediction (based on historical data) and live traffic into account. To this end, we propose a practical algorithm that, while robust to user preferences, is able to integrate global changes of the time-dependent metric~(e.g., due to traffic updates or user restrictions) faster than previous approaches, while allowing subsequent queries that enable interactive applications

Engineering Algorithms for Dynamic and Time-Dependent Route Planning

Efficiently computing shortest paths is an essential building block of many mobility applications, most prominently route planning/navigation devices and applications. In this thesis, we apply the algorithm engineering methodology to design algorithms for route planning in dynamic (for example, considering real-time traffic) and time-dependent (for example, considering traffic predictions) problem settings. We build on and extend the popular Contraction Hierarchies (CH) speedup technique. With a few minutes of preprocessing, CH can optimally answer shortest path queries on continental-sized road networks with tens of millions of vertices and edges in less than a millisecond, i.e. around four orders of magnitude faster than Dijkstra’s algorithm. CH already has been extended to dynamic and time-dependent problem settings. However, these adaptations suffer from limitations. For example, the time-dependent variant of CH exhibits prohibitive memory consumption on large road networks with detailed traffic predictions. This thesis contains the following key contributions: First, we introduce CH-Potentials, an A*-based routing framework. CH-Potentials computes optimal distance estimates for A* using CH with a lower bound weight function derived at preprocessing time. The framework can be applied to any routing problem where appropriate lower bounds can be obtained. The achieved speedups range between one and three orders of magnitude over Dijkstra’s algorithm, depending on how tight the lower bounds are. Second, we propose several improvements to Customizable Contraction Hierarchies (CCH), the CH adaptation for dynamic route planning. Our improvements yield speedups of up to an order of magnitude. Further, we augment CCH to efficiently support essential extensions such as turn costs, alternative route computation and point-of-interest queries. Third, we present the first space-efficient, fast and exact speedup technique for time-dependent routing. Compared to the previous time-dependent variant of CH, our technique requires up to 40 times less memory, needs at most a third of the preprocessing time, and achieves only marginally slower query running times. Fourth, we generalize A* and introduce time-dependent A* potentials. This allows us to design the first approach for routing with combined live and predicted traffic, which achieves interactive running times for exact queries while allowing live traffic updates in a fraction of a minute. Fifth, we study extended problem models for routing with imperfect data and routing for truck drivers and present efficient algorithms for these variants. Sixth and finally, we present various complexity results for non-FIFO time-dependent routing and the extended problem models

Towards Mobile Time-Dependent Route Planning

Road networks with time-dependent edge weights can describe rush hours and similar regular changes in traffic over a day. Optimal routes can be calculated efficiently using time-dependent Contraction Hierarchies. On mobile devices it is usually not possible and also not reasonable to hold the entire data in the limited main memory. Therefore the main performance bottleneck is the data access on the flash memory, which can only be read blockwise. For fast route query calculations, the number of accessed blocks has to be low. To achieve this, we first reduce the amount of data using a lossy compression. This introduces inaccuracies in the calculations hence not always the optimal route is chosen. Nevertheless using this method the result is still nearly exact because the average introduced delay compared to the optimal route is less than 0.001%. In the worst case a delay of about 0.1% occurs which still is too small to be noticed. Second, the data is rearranged in a way that increases the locality. This leads to a lower number of required block loads. For a road network of Germany we can answer random route queries with an average of 102 block loads. Assuming that a block access takes 1.3 ms, this can be done in 133 ms. Users perceive this as a nearly instant reaction. Everyday route calculations tend to be even smaller and can be calculated faster

Time-Dependent Route Planning with Contraction Hierarchies

Design and experimental evaluation of route planning algorithms for time-dependent road networks, which model regular effects like congestions. By generalizing contraction hierarchies, we achieve fast and space efficient computation of minimum travel time routes and profiles. We also consider additional constant costs (e.g., to penalize detours and motorway tolls), which makes route planning NP-hard. Then, routes become heuristic, but we get quite near to the optimum as experiments show

Моделювання залежних від часу проблем пошуку оптимальних маршрутів: огляд

Розглянуто задачі пошуку оптимальних маршрутів мережами громадського транспорту. Наведено підходи до подання розкладу за допомогою графів у залежних від часу задачах пошуку оптимальних шляхів для залізничних і авіамереж. Проаналізовано типові задачі пошуку оптимальних шляхів у залежних від часу мережах.Рассмотрены задачи поиска оптимальных маршрутов сетями общественного транспорта. Приведены подходы для представления расписания с помощью графов в зависимых от времени задачах поиска оптимальных путей для железнодорожных и авиасетей. Проанализированы типовые задачи поиска оптимальных путей в зависимых от времени сетях.We consider the problem of optimal dynamic time-dependent route planning in public transport networks. The paper describes approaches to represent schedule within graphs for the time-dependent shortest path problems in rail and air networks. Common types of timedependent shortest path problems in dynamic networks are reviewed

Compressed Transmission of Route Descriptions

We present two methods to compress the description of a route in a road network, i.e., of a path in a directed graph. The first method represents a path by a sequence of via edges. The subpaths between the via edges have to be unique shortest paths. Instead of via edges also via nodes can be used, though this requires some simple preprocessing. The second method uses contraction hierarchies to replace subpaths of the original path by shortcuts. The two methods can be combined with each other. Also, we propose the application to mobile server based routing: We compute the route on a server which has access to the latest information about congestions for example. Then we transmit the computed route to the car using some mobile radio communication. There, we apply the compression to save costs and transmission time. If the compression works well, we can transmit routes even when the bandwidth is low. Although we have not evaluated our ideas with realistic data yet, they are quite promising.Comment: 7 pages, technical repor

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