Work

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

Year: 2010

Type: article

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.

Source: Statistical Science

DOI: 10.1214/10-sts335

Authors: David J. Aldous, Julian Shun

Institutions: Carnegie Mellon University, University of California, Berkeley

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: Large Random Structures and Network Flow