Transit node routing: Difference between revisions

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In [[applied mathematics]], '''transit node routing''' can be used to speed up [[Shortest path routing|shortest-path routing]] by pre-computing connections between common access nodes to a sub-network relevant to long-distance travel.<ref name=":0">{{Cite journal|lastlast1=Bast|firstfirst1=H.|last2=Funke|first2=S.|last3=Sanders|first3=P.|last4=Schultes|first4=D.|date=2007-04-27|title=Fast Routing in Road Networks with Transit Nodes|journal=Science|volume=316|issue=5824|pages=566|doi=10.1126/science.1137521|pmid=17463281|issn=0036-8075|bibcode=2007Sci...316..566B|s2cid=16559205 }}</ref>
 
Transit node routing as a framework was established in 2007<ref name=":0" /> and many concrete implementations have surfaced in the years after such as approaches using grids, highway hierarchies<ref name=":1" /> and [[contraction hierarchies]].<ref name=":2" /> Transit node routing is a static approach that requires pre-processing of pair-wise distances between important nodes in the graph (see below how those nodes are chosen). A dynamic approach has not been published.<ref>{{Citation|lastlast1=Schultes|firstfirst1=Dominik|chapter=Dynamic Highway-Node Routing|pages=66–79|publisher=Springer Berlin Heidelberg|isbn=9783540728443|last2=Sanders|first2=Peter|doi=10.1007/978-3-540-72845-0_6|title=Experimental Algorithms|volume=4525|series=Lecture Notes in Computer Science|year=2007}}</ref>
 
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* How should local queries be handled?
 
The following example implementations of this framework answer these questions using different underlying methods such as grouping nodes in cells of an overlay [[Grid (spatial index)|grid]]<ref name=":1">{{Citation|lastlast1=Bast|firstfirst1=Holger|title=In Transit to Constant Time Shortest-Path Queries in Road Networks|date=2007-01-06|work=2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX)|pages=46–59|publisher=Society for Industrial and Applied Mathematics|isbn=9781611972870|last2=Funke|first2=Stefan|last3=Matijevic|first3=Domagoj|last4=Sanders|first4=Peter|last5=Schultes|first5=Dominik|doi=10.1137/1.9781611972870.5|doi-access=free}}</ref> and a more sophisticated implementation based on [[contraction hierarchies]].<ref name=":2">{{Citation|lastlast1=Arz|firstfirst1=Julian|title=Transit Node Routing Reconsidered|date=2013|work=Experimental Algorithms|pages=55–66|publisher=Springer Berlin Heidelberg|isbn=9783642385261|last2=Luxen|first2=Dennis|last3=Sanders|first3=Peter|arxiv=1302.5611|doi=10.1007/978-3-642-38527-8_7|bibcode=2013arXiv1302.5611A|s2cid=14371800 }}</ref>
 
=== Geometrical approach using grids===