Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms

In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway dimension and diameter for the current fastest routing algorithms, including contraction hierarchies, transit node routing, and hub labeling. In this paper, we show corresponding lower bounds for the same three algorithms. We also show how to improve a result by Milosavljevic which lower bounds the number of shortcuts added in the preprocessing stage for contraction hierarchies. We relax the assumption of an optimal contraction order (which is NP-hard to compute), allowing the result to be applicable to real-world instances. Finally, we give a proof that optimal preprocessing for hub labeling is NP-hard. Hardness of optimal preprocessing is known for most routing algorithms, and was suspected to be true for hub labeling

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

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

Engineering Algorithms for Route Planning in Multimodal Transportation Networks

Practical algorithms for route planning in transportation networks are a showpiece of successful Algorithm Engineering. This has produced many speedup techniques, varying in preprocessing time, space, query performance, simplicity, and ease of implementation. This thesis explores solutions to more realistic scenarios, taking into account, e.g., traffic, user preferences, public transit schedules, and the options offered by the many modalities of modern transportation networks

Algorithm Engineering for Realistic Journey Planning in Transportation Networks

Diese Dissertation beschäftigt sich mit der Routenplanung in Transportnetzen. Es werden neue, effiziente algorithmische Ansätze zur Berechnung optimaler Verbindungen in öffentlichen Verkehrsnetzen, Straßennetzen und multimodalen Netzen, die verschiedene Transportmodi miteinander verknüpfen, eingeführt. Im Fokus der Arbeit steht dabei die Praktikabilität der Ansätze, was durch eine ausführliche experimentelle Evaluation belegt wird

Building Blocks for Mapping Services

Mapping services are ubiquitous on the Internet. These services enjoy a considerable user base. But it is often overlooked that providing a service on a global scale with virtually millions of users has been the playground of an oligopoly of a select few service providers are able to do so. Unfortunately, the literature on these solutions is more than scarce. This thesis adds a number of building blocks to the literature that explain how to design and implement a number of features

Advanced Route Planning in Transportation Networks

We present fast and efficient algorithms for routing in road and public transit networks. An algorithm for public transit can handle very large and poorly structured networks in a fully realistic scenario. Algorithms to answer flexible shortest path queries consider additional query parameters, such as edge weight or restrictions. Finally, specialized algorithms compute sets of related shortest path distances for time-dependent distance table computation, ride sharing and closest POI location

Comparative Study of Speed-Up Routing Algorithms in Road Networks

We study the problem of finding the shortest distance and the shortest path from one node to another in graphs modeling large road networks. Classical algorithms like Dijkstra and Astar do not have good performance in such networks. In recent years, two new approaches called Contraction Hierarchy and Hub Labeling which use preprocessing to generate auxiliary data to improve the query time performance were proposed, and many variants have followed. These algorithms are very efficient on large networks when a large number of queries is expected. In the literature, these algorithms are called speed-up algorithms. More recently, dynamic routing algorithms have been proposed, such as Customizable Contraction Hierarchy and Dynamic Hierarchical Hub Labeling. These are designed to respond efficiently to edge weight changes resulting from changes in traffic. In this thesis, we present an experimental study of the performance of the above static and dynamic routing algorithms on two different road networks, in terms of travel time and query processing time. Our results show that Customizable Contraction Hierarchy is the best for shortest path query in both the static and dynamic settings, while Hub Labeling is the most efficient in answering shortest distance queries in the static setting. We also show that Dynamic Hub Labeling’s edge weight update operations are inefficient in practice