Math @ Duke

Publications [#235496] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Apfelbaum, R; Purdy, G; Sharir, M, Similar simplices in a ddimensional point set,
Proceedings of the Annual Symposium on Computational Geometry
(2007),
pp. 232238 [doi]
(last updated on 2017/12/11)
Abstract: We consider the problem of bounding the maximum possible number f k,d(n) of ksimplices 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 d2, d(n) = O(n d8/5) and f d1,d(n) = O *(n d72/55), 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.


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