Statistical Science

Connected Spatial Networks over Random Points and a Route-Length Statistic

David J. Aldous and Julian Shun

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Abstract

We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. 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 proximity 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 2007–2009.

Article information

Source
Statist. Sci., Volume 25, Number 3 (2010), 275-288.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.ss/1294167960

Digital Object Identifier
doi:10.1214/10-STS335

Mathematical Reviews number (MathSciNet)
MR2791668

Zentralblatt MATH identifier
1329.60009

Keywords
Proximity graph random graph spatial network geometric graph

Citation

Aldous, David J.; Shun, Julian. Connected Spatial Networks over Random Points and a Route-Length Statistic. Statist. Sci. 25 (2010), no. 3, 275--288. doi:10.1214/10-STS335. https://projecteuclid.org/euclid.ss/1294167960


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