Limit theory for the random on-line nearest-neighbor graph

In the on‐line nearest‐neighbor graph (ONG), each point after the first in a sequence of points in ℝd is joined by an edge to its nearest neighbor amongst those points that precede it in the sequence. We study the large‐sample asymptotic behavior of the total power‐weighted length of the ONG on unif...

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Bibliographic Details
Published in:Random structures & algorithms Vol. 32; no. 2; pp. 125 - 156
Main Authors: Penrose, Mathew D., Wade, Andrew R.
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.03.2008
Subjects:
divide-and-conquer
fixed-point equation
nearest-neighbor graph
spatial network evolution
weak convergence
ISSN:1042-9832, 1098-2418
Online Access:Get full text
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Summary:In the on‐line nearest‐neighbor graph (ONG), each point after the first in a sequence of points in ℝd is joined by an edge to its nearest neighbor amongst those points that precede it in the sequence. We study the large‐sample asymptotic behavior of the total power‐weighted length of the ONG on uniform random points in (0,1)d. In particular, for d = 1 and weight exponent α > 1/2, the limiting distribution of the centered total weight is characterized by a distributional fixed‐point equation. As an ancillary result, we give exact expressions for the expectation and variance of the standard nearest‐neighbor (directed) graph on uniform random points in the unit interval. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008
Bibliography:EPSRC
ArticleID:RSA20185
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ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20185