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Publications [#235496] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Apfelbaum, R; Purdy, G; Sharir, M, Similar simplices in a d-dimensional point set, Proceedings of the Annual Symposium on Computational Geometry (October, 2007), pp. 232-238 [doi]
    (last updated on 2018/11/18)

    We consider the problem of bounding the maximum possible number fk,d(n) of k-simplices that are spanned by a set of n pointsin Rdand are similar to a given simplex. We first show that f2,3(n) = O(n13/6), and then tacklethe general case, and show that fd-2, d(n) = O(nd-8/5) and fd-1,d(n) = O*(nd-72/55), for any d.Our technique extends to derive bounds for other valuesof k and d, and we illustrate this by showing that f2,5(n)=O(n8/3). Copyright 2007 ACM.
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