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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Vydáno v:Random structures & algorithms Ročník 32; číslo 2; s. 125 - 156
Hlavní autoři: Penrose, Mathew D., Wade, Andrew R.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.03.2008
Témata:
divide-and-conquer
fixed-point equation
nearest-neighbor graph
spatial network evolution
weak convergence
ISSN:1042-9832, 1098-2418
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Shrnutí: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
Bibliografie:EPSRC
ArticleID:RSA20185
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SourceType-Scholarly Journals-1
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content type line 23
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20185