Abstract:In this paper, for d ∈ N, we study the online nearest neighbor random tree in dimension d (d-NN tree for short) defined as follows. Fix the flat torus T d n of dimension d and area n, equipped with the metric inherited from the Euclidean metric of R d . Then, embed consecutively n vertices in T d n uniformly at random and let each vertex but the first one connect to its (already embedded) nearest neighbor. We show that a.a.s. the number of vertices of degree at least k ∈ N in the d-NN tree decreases exponentia… Show more
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