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Statistical Science 2010, Vol. 25, No. 3, 275288

Summary: Statistical Science
2010, Vol. 25, No. 3, 275288
DOI: 10.1214/10-STS335
Institute of Mathematical Statistics, 2010
Connected Spatial Networks over Random
Points and a Route-Length Statistic
David J. Aldous and Julian Shun
Abstract. We review mathematically tractable models for connected net-
works on random points in the plane, emphasizing the class of proximity
graphs which deserves to be better known to applied probabilists and statisti-
cians. We introduce and motivate a particular statistic R measuring shortness
of routes in a network. We illustrate, via Monte Carlo in part, the trade-off
between normalized network length and R in a one-parameter family of prox-
imity graphs. How close this family comes to the optimal trade-off over all
possible networks remains an intriguing open question.
The paper is a write-up of a talk developed by the first author during 2007
Key words and phrases: Proximity graph, random graph, spatial network,
geometric graph.


Source: Aldous, David J. - Department of Statistics, University of California at Berkeley


Collections: Mathematics