Similar simplices in a d-dimensional point set
We consider the problem of bounding the maximum possible number f k,d(n) of k-simplices that are spanned by a set of n pointsin R d and are similar to a given simplex. We first show that f 2,3(n) = O(n 13/6), and then tacklethe general case, and show that f d-2, d(n) = O(n d-8/5) and f d-1,d(n) = O *(n d-72/55), for any d.Our technique extends to derive bounds for other valuesof k and d, and we illustrate this by showing that f 2,5(n)=O(n 8/3). Copyright 2007 ACM.
Agarwal, PK; Apfelbaum, R; Purdy, G; Sharir, M
Proceedings of the Annual Symposium on Computational Geometry
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