2004
DOI: 10.1007/s00454-004-1120-8
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Abstract: Abstract. We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some Euclidean space R d . We assume that M is known to us only through a finite sample P ⊂ M, as is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most min{2 O(k) n, n 2 }, where n = |P| and k = dim M, as opposed to the n d/2 complexity of the Delaunay triangulation, which is often used to model manifolds. We prove that we can…

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