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Abstract: We show that in the worst case, Ω(n^(d/2-1) + n log n) sidedness queries are required to determine whether the convex hull of n points in R^d is simplicial, or to determine the number of convex hull facets. This lower bound matches known upper bounds in any odd dimension. Our result follows from a straightforward adversary argument. A key step in the proof is the construction of a quasi-simplicial n-vertex polytope with Ω(n^(d/2-1)) degenerate facets. While it has been known for... (Update)
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BibTeX entry: (Update)
J. Erickson. New lower bounds for convex hull problems in odd dimensions. In Proc. 12th Ann. ACM Symp. Comput. Geom., pages 1--9, 1996. http://citeseer.ist.psu.edu/article/erickson96new.html More
@inproceedings{ erickson96new,
author = "Jeff Erickson",
title = "New Lower Bounds for Convex Hull Problems in Odd Dimensions",
booktitle = "Symposium on Computational Geometry",
pages = "1--9",
year = "1996",
url = "citeseer.ist.psu.edu/article/erickson96new.html" }
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