In Transit to Constant Time Shortest-Path Queries in Road Networks

Abstract

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 develop an algorithmic approach-transit node routingthat allows us to reduce quickest-path queries in road networks to a small number of table lookups. We present two implementations of this idea, one based on a simple grid data structure and one based on highway hierarchies. For the road map of the United States, our best query times improve over the best previously published figures by two orders of magnitude. Our results exhibit various trade-offs between average query time (6 µs to 63 µs), preprocessing time (62 min to 1200 min), and storage overhead (27 bytes/node to 247 bytes/node).

Engineering Route Planning Algorithms

“…Independently, three approaches proved successful for selecting transit nodes: separators [51,15], border nodes of a partition [3,4,2], and nodes categorized as important by other speedup techniques [3,4,61]. It turns out that for route planning in road networks, the latter approach is the most promising one.…”

“…(The original implementation cannot directly measure this because it has large overheads for disk access and parsing of XML-data). Independently, transit-node routing was developed [3], that lifts the speedup to six orders of magnitude and completely replaces Dijkstra-like search by table lookups. This approach was further accelerated by combining transit nodes with edge flags [8], yielding speedups of over 3 millions.…”

“…In several applications we need complete distance tables between specified sets of source nodes S and target nodes T . For example, in logistics optimization, traffic simulation, and also within preprocessing techniques [46,3]. Many non-goal-directed bidirectional search methods [67,26,65]) can be adapted in such a way that only a single forward search from each source node and a single backward search from each target node is needed [42].…”

“…The efficiency of many speedup techniques stems from introducing shortcut edges and distance table entries that replace entire paths in the original graph [67,58,26,59,51,3]. A disadvantage of these approaches is that the search will output only a 'summary description' of the optimal path that involves shortcuts.…”

“…A disadvantage of these approaches is that the search will output only a 'summary description' of the optimal path that involves shortcuts. Fortunately, it is quite straightforward to augment the shortcuts with information for unpacking them [17,42,3,23,62]. Since one can afford to precompute unpacked representations of the most frequently needed long-distance shortcuts, outputting the path turns out to be up to four times faster than just traversing the edges in the original graph.…”