Constructing the relative neighborhood graph in 3-dimensional Euclidean space

Constructing the relative neighborhood graph in 3-dimensional Euclidean space

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Article ID: iaor19912051
Country: Netherlands
Volume: 31
Issue: 2
Start Page Number: 181
End Page Number: 191
Publication Date: Apr 1991
Journal: Discrete Applied Mathematics
Authors: ,
Abstract:

The relative neighborhood graph for a finite set equ1 of points, briefly RNG(S), is defined by the following formation rule: equ2 is an edge in RNG(S) if and only if for allequ3. The authors show that RNG for point sets in equ4equ5can be constructed in optimal space and equ6 time. Also, combinatorial estimates on the size of RNG in equ7are given.

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