Results 1 
2 of
2
Connected Spatial Networks over Random Points and a RouteLength Statistic
"... 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 r ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
(Show Context)
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 tradeoff between normalized network length and R in a oneparameter family of proximity graphs. How close this family comes to the optimal tradeoff over all possible networks remains an intriguing open question. The paper is a writeup of a talk developed by the first author during 2007– 2009. Key words and phrases: Proximity graph, random graph, spatial network,
Models for Connected Networks over Random Points and a RouteLength Statistic
, 2009
"... We review mathematically tractable models for connected networks on random points in the plane, emphasising the littlestudied class of proximity graphs and introducing a new model called the Hammersley network. We introduce and motivate a particular statistic R measuring shortness of routes in a ne ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
We review mathematically tractable models for connected networks on random points in the plane, emphasising the littlestudied class of proximity graphs and introducing a new model called the Hammersley network. We introduce and motivate a particular statistic R measuring shortness of routes in a network. We show (via Monte Carlo, in part) the tradeoff between normalized network length and R in a oneparameter family of proximity graphs. How close this family comes to the optimal tradeoff over all possible networks remains an intriguing open question. This material has been presented in talks since 2007. It will be periodically updated as technical papers [3, 4, 7, 8] are completed, and ultimately published as some kind of survey.