Graphs on uniform points in [0,1]d

Martin J. B. Appel; Ralph P. Russo; King Jang Yang

doi:10.1117/12.211354

20 June 1995 Graphs on uniform points in [0,1]^d

Martin J. B. Appel, Ralph P. Russo, King Jang Yang

Proceedings Volume 2496, Detection Technologies for Mines and Minelike Targets; (1995) https://doi.org/10.1117/12.211354
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

Statistical problems in pattern or structure recognition for a random multidimensional point set may be addressed by variations on the random graph model of Erdos and Renyui. The imposition of graph structure with a variable edge criterion on a large random point set allows a search for signature quantities or behavior under the given distributional hypothesis. The work is motivated by the question of how to make statistical inferences from sensed mine field data. This article describes recent results obtained in the following special cases. On independent random points U₁,...,U_n distributed uniformly on [0,1]^d, a random graph G_n(x) is constructed in which two distinct such points are joined by an edge if the l_(infinity )-distance between them is at most some prescribed value 0 n, the smallest x such that G_n(x) is connected, and the largest nearest neighbor link d_n, the smallest x such that G_n(x) has no vertices of degree zero, are asymptotic in ratio, as n becomes large, for d >= 2.

Citation Download Citation

Martin J. B. Appel, Ralph P. Russo, and King Jang Yang "Graphs on uniform points in [0,1]^d", Proc. SPIE 2496, Detection Technologies for Mines and Minelike Targets, (20 June 1995); https://doi.org/10.1117/12.211354

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