The highway dimension is a graph parameter modelling transportation networks, such as road networks or public transportation networks. It was first formally defined by Abraham et al.[1] based on the observation by Bast et al.[2][3] that any road network has a sparse set of "transit nodes", such that driving from a point A to a sufficiently far away point B along the shortest route will always pass through one of these transit nodes. It has also been proposed that the highway dimension captures the properties of public transportation networks well (at least according to definitions 1 and 2 below), given that longer routes using busses, trains, or airplanes will typically be serviced by larger transit hubs (stations and airports). This relates to the spoke–hub distribution paradigm in transport topology optimization.
^Abraham, Ittai; Fiat, Amos; Goldberg, Andrew V.; Werneck, Renato F. (2010-01-17). Highway Dimension, Shortest Paths, and Provably Efficient Algorithms. Society for Industrial and Applied Mathematics. pp. 782–793. doi:10.1137/1.9781611973075.64. ISBN 978-0-89871-701-3. S2CID 9330775.
^Bast, Holger; Funke, Stefan; Matijevic, Domagoj; Sanders, Peter; Schultes, Dominik (2007-01-06), Applegate, David; Stølting Brodal, Gerth (eds.), "In Transit to Constant Time Shortest-Path Queries in Road Networks", 2007 Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX), Philadelphia, PA: Society for Industrial and Applied Mathematics, pp. 46–59, doi:10.1137/1.9781611972870.5, ISBN 978-1-61197-287-0, retrieved 2023-11-10
^Bast, Holger; Funke, Stefan; Matijevic, Domagoj; Demetrescu, Camil; Goldberg, Andrew; Johnson, David (2006). "TRANSIT: Ultrafast Shortest-Path Queries with Linear-Time Preprocessing". The Shortest Path Problem: Ninth DIMACS Implementation Challenge.
The highwaydimension is a graph parameter modelling transportation networks, such as road networks or public transportation networks. It was first formally...
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