Fast Routing in Road Networks with Transit Nodes

Bast, Hannah; Funke, Stefan; Sanders, Peter; Schultes, Dominik

doi:10.1126/science.1137521

Cited by 185 publications

(110 citation statements)

References 1 publication

Supporting

Mentioning

110

Contrasting

Order By: Relevance

“…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.…”

Section: Highway-node Routing (Hnr)mentioning

confidence: 99%

Engineering Route Planning Algorithms

Delling

Sanders

Schultes

et al. 2009

Lecture Notes in Computer Science

Self Cite

362

235

View full text Add to dashboard Cite

Abstract. Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra's algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, time-dependent routing, and flexible objective functions.

show abstract

Section: Highway-node Routing (Hnr)mentioning

confidence: 99%

Engineering Route Planning Algorithms

Delling

Sanders

Schultes

et al. 2009

Lecture Notes in Computer Science

Self Cite

362

235

View full text Add to dashboard Cite

show abstract

“…1. Our work has indirect connections with some actual algorithms used by automobile global positioning system devices to find routes. One key idea (13) is that there is a set of about 10,000 major road intersections in the United States (they write "transit nodes") with the property that, unless the start and destination points are close, the shortest route goes via some transit node near the start and some transit node near the destination. Given such a set, one can precompute shortest routes and route lengths between each pair of transit nodes, and then answer a query by using the classical algorithm to calculate route lengths from starting (and from destination) point to each nearby transit node, and finally minimize over pairs of such transit nodes.…”

Section: Future Work: Connections and Analogiesmentioning

confidence: 99%

True scale-invariant random spatial networks

Aldous

Ganesan

2013

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Some aspects of real-world road networks seem to have an approximate scale invariance property, motivating study of mathematical models of random networks whose distributions are exactly invariant under Euclidean scaling. This requires working in the continuum plane, so making a precise definition is not trivial. We introduce an axiomatization of a class of processes we call scaleinvariant random spatial networks, whose primitives are routes between each pair of points in the plane. One concrete model, based on minimum-time routes in a binary hierarchy of roads with different speed limits, has been shown to satisfy the axioms, and two other constructions (based on Poisson line processes and on dynamic proximity graphs) are expected also to do so. We initiate study of structure theory and summary statistics for general processes in the class. Many questions arise in this setting via analogies with diverse existing topics, from geodesics in first-passage percolation to transit node-based route-finding algorithms.W e introduce and study a mathematical structure inspired by road networks. Although not intended as literally realistic, we do believe it raises and illustrates several interesting conceptual points and potential connections with other fields, summarized in the final section. Details will appear in a long technical paper (1). Here, we seek to explain in words rather than mathematical symbols.Consider two differences between traditional paper maps and modern online maps for roads, which will motivate two conceptual features of our model. On paper, one needs different maps for different scales-for the intercity network and for the street network in one town. The usual simplified mathematical models involve different mathematical objects at the two scales, for instance representing cities as points for an intercity network model (2). Online maps allow you to "zoom in" so that the window you see covers less real-world area but shows more detail, specifically (for our purpose) showing comparatively minor roads that are not shown when you "zoom out" again. As a first conceptual feature, we seek a mathematical model that represents roads consistently over all scales. Next, a paper map shows roads, and the user then chooses a "route" between start and destination. In contrast, a typical use of an online map is to enter the start and destination address and receive a suggested route. As a second conceptual feature, our model will treat routes as the basic objects. That is, somewhat paradoxically, in our model routes determine roads.Returning to the image of zooming in and out, the key assumption in our models is that statistical features of what we see in the map inside a window do not depend on the real-world width of the region being shown-on whether it is 5 miles or 500 miles. We call this property "scale invariance," in accord with the usual meaning of that phrase within physics. Of course, our phrase "what we see" is very vague; we mean quantifiable aspects of the road network, and this is best understood via...

show abstract

“…Storing the all-pairs shortest-path data [4] can reduce the cost of planning to constant time, given that there is space to store this data. This data can be compressed in many different ways [5][6][7]; the effectiveness of each method depends on the topology of the map. These approaches often maintain optimal paths relative to the representation of the state space being used.…”

Section: Single-agent Searchmentioning

confidence: 99%

Moving Path Planning Forward

Sturtevant

2012

Motion in Games

View full text Add to dashboard Cite

Abstract. Path planning technologies have rapidly improved over the last 10 years, but further integration is needed if pathfinding engines are to drive the behavior of even more realistic characters. This paper briefly outlines existing approaches for path planning and suggests scenarios where integration of information about character's relationships could improve the quality of path planning in games.

show abstract

Fast Routing in Road Networks with Transit Nodes

Cited by 185 publications

References 1 publication

Engineering Route Planning Algorithms

Engineering Route Planning Algorithms

True scale-invariant random spatial networks

Moving Path Planning Forward

Contact Info

Product

Resources

About