Similar simplices in a d-dimensional point set
Publication
, Journal Article
Agarwal, PK; Apfelbaum, R; Purdy, G; Sharir, M
Published in: Proceedings of the Annual Symposium on Computational Geometry
October 22, 2007
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.
Published In
Proceedings of the Annual Symposium on Computational Geometry
DOI
Publication Date
October 22, 2007
Start / End Page
232 / 238
Citation
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Agarwal, P. K., Apfelbaum, R., Purdy, G., & Sharir, M. (2007). Similar simplices in a d-dimensional point set. Proceedings of the Annual Symposium on Computational Geometry, 232–238. https://doi.org/10.1145/1247069.1247112
Agarwal, P. K., R. Apfelbaum, G. Purdy, and M. Sharir. “Similar simplices in a d-dimensional point set.” Proceedings of the Annual Symposium on Computational Geometry, October 22, 2007, 232–38. https://doi.org/10.1145/1247069.1247112.
Agarwal PK, Apfelbaum R, Purdy G, Sharir M. Similar simplices in a d-dimensional point set. Proceedings of the Annual Symposium on Computational Geometry. 2007 Oct 22;232–8.
Agarwal, P. K., et al. “Similar simplices in a d-dimensional point set.” Proceedings of the Annual Symposium on Computational Geometry, Oct. 2007, pp. 232–38. Scopus, doi:10.1145/1247069.1247112.
Agarwal PK, Apfelbaum R, Purdy G, Sharir M. Similar simplices in a d-dimensional point set. Proceedings of the Annual Symposium on Computational Geometry. 2007 Oct 22;232–238.
Published In
Proceedings of the Annual Symposium on Computational Geometry
DOI
Publication Date
October 22, 2007
Start / End Page
232 / 238