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

Penrose, Mathew D. and Wade, Andrew R. (2008) 'Limit theory for the random on-line nearest-neighbor graph.', Random structures and algorithms., 32 (2). pp. 125-156.


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.

Item Type:Article
Keywords:Nearest-neighbor graph,Spatial network evolution, Weak convergence, Fixed-point equation, Divide-and-conquer.
Full text:Full text not available from this repository.
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Date accepted:No date available
Date deposited:No date available
Date of first online publication:March 2008
Date first made open access:No date available

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