Random Road Networks: The Quadtree Model

What does a typical road network look like? Existing generative models tend to focus on one aspect to the exclusion of others. We introduce the general-purpose \emph{quadtree model} and analyze its shortest paths and maximum flow.

[1]  Éric Fusy,et al.  Uniform random sampling of planar graphs in linear time , 2007, Random Struct. Algorithms.

[2]  Gilles Schaeffer,et al.  Random sampling of large planar maps and convex polyhedra , 1999, STOC '99.

[3]  David Eppstein,et al.  Studying (non-planar) road networks through an algorithmic lens , 2008, GIS '08.

[4]  Amos Fiat,et al.  Highway dimension, shortest paths, and provably efficient algorithms , 2010, SODA '10.

[5]  A. Goldberg,et al.  TRANSIT: Ultrafast Shortest-Path Queries with Linear-Time Preprocessing , 2006 .

[6]  A. P. Masucci,et al.  Random planar graphs and the London street network , 2009, 0903.5440.

[7]  Michael Mitzenmacher,et al.  A Brief History of Generative Models for Power Law and Lognormal Distributions , 2004, Internet Math..

[8]  Jean Bertoin,et al.  Random fragmentation and coagulation processes , 2006 .

[9]  Philip N. Klein,et al.  An O (n log n) algorithm for maximum st-flow in a directed planar graph , 2006, SODA '06.

[10]  Greg N. Frederickson,et al.  Fast Algorithms for Shortest Paths in Planar Graphs, with Applications , 1987, SIAM J. Comput..

[11]  Peter Elias,et al.  A note on the maximum flow through a network , 1956, IRE Trans. Inf. Theory.

[12]  R. Tarjan,et al.  A Separator Theorem for Planar Graphs , 1977 .

[13]  Luc Devroye,et al.  A note on the height of binary search trees , 1986, JACM.

[14]  Anusch Taraz,et al.  The random planar graph process , 2008, Random Struct. Algorithms.

[15]  David Eppstein,et al.  Going off-road: transversal complexity in road networks , 2009, GIS.

[16]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956 .

[17]  A. Clauset,et al.  Scale invariance in road networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.