A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a graph. In the past there has been a succession of techniques that infer a more and more fine grained hierarchy enabling increasingly more efficient queries. This appeared to culminate in contraction hierarchies that assign one hierarchy level to each vertex. In this paper we show how to identify an even more fine grained hierarchy that assigns one level to each edge of the network. Our findings indicate that this can lead to considerably smaller search spaces in terms of visited edges. Currently, this does not result in improved query times so that it remains an open question whether these edge hierarchies can lead to overall improved performance. However, we believe that the technique as such is a noteworthy enrichment of the portfolio of available techniques that might prove useful in the future.
There has been a lot of work on route planning. Refer to @cite_11 for a recent overview. Here we only give selected references to place EHs into the big picture. Besides hierarchical route planning techniques there are also techniques which direct the shortest path search towards the goal (e.g., landmarks @cite_16 , precomputed cluster distances @cite_0 , arc flags @cite_20 ). On road networks goal directed techniques are usually inferior to hierarchical ones since they need considerably more query or preprocessing time. However, combining goal directed and hierarchical route planning is a useful approach @cite_16 @cite_2 . We expect that this is also possible for EHs using the same techniques as used before. Other techniques allow very fast queries by building shortest paths directly from two (hub labeling @cite_12 ) or three (transit node routing @cite_5 @cite_3 ) precomputed shortcuts without requiring a graph search. However, these methods require considerably more space than EHs.
@cite_3 @cite_0 @cite_2 @cite_5 @cite_16 @cite_12 @cite_20 @cite_11
1601313669 2132044905 2150418461 2083019227 2151400766 2112513979 1559814459 2104317982
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 contraction hierarchy (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 problem. We demonstrate how Dijkstra's algorithm for shortest path queries can be accelerated by using precomputed shortest path distances. Our approach allows a completely flexible tradeoff between query time and space consumption for precomputed distances. In particular, sublinear space is sufficient to give the search a strong “sense of direction”. We evaluate our approach experimentally using large, real-world road networks. In recent years, highly effective hierarchical and goal-directed speed-up techniques for routing in large road networks have been developed. This article makes a systematic study of combinations of such techniques. These combinations turn out to give the best results in many scenarios, including graphs for unit disk graphs, grid networks, and time-expanded timetables. Besides these quantitative results, we obtain general insights for successful combinations. When you drive to somewhere far away, you will leave your current location via one of only a few important traffic junctions. Starting from this informal observation, we developed an algorithmic approach, transit node routing, that allows us to reduce quickest path queries in road networks to a small number of table lookups. For road maps of Western Europe and the United States, our best query times improved over the best previously published figures by two orders of magnitude. This is also more than one million times faster than the best known algorithm for general networks. We study the point-to-point shortest path problem in a setting where preprocessing is allowed. We improve the reach-based approach of Gutman [17] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs to reduce vertex reaches. Our modifications greatly improve both preprocessing and query times. The resulting algorithm is as fast as the best previous method, due to Sanders and Schultes [28]. However, our algorithm is simpler and combines in a natural way with A* search, which yields significantly better query times. [SODA 2010] have recently presented a theoretical analysis of several practical point-to-point shortest path algorithms based on modeling road networks as graphs with low highway dimension. They also analyze a labeling algorithm. While no practical implementation of this algorithm existed, it has the best time bounds. This paper describes an implementation of the labeling algorithm that is faster than any existing method on continental road networks. In this paper, we consider Dijkstra's algorithm for the point-to-point shortest path problem in large and sparse graphs with a given layout. In [1], a method has been presented that uses a partitioning of the graph to perform a preprocessing which allows to speed-up Dijkstra's algorithm considerably. We present an experimental study that evaluates which partitioning methods are suited for this approach. In particular, we examine partitioning algorithms from computational geometry and compare their impact on the speed-up of the shortest-path algorithm. Using a suited partitioning algorithm speed-up factors of 500 and more were achieved. Furthermore, we present an extension of this speed-up technique to multiple levels of partitionings. With this multi-level variant, the same speed-up factors can be achieved with smaller space requirements. It can therefore be seen as a compression of the precomputed data that conserves the correctness of the computed shortest paths. 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.