On the Size of Higher-Dimensional Triangulations
نویسنده
چکیده
I show that there are sets of n points in three dimensions, in general position, such that any triangulation of these points has only O(n5/3) simplices. This is the first nontrivial upper bound on the MinMax triangulation problem posed by Edelsbrunner, Preparata and West in 1990: What is the minimum over all general-position point sets of the maximum size of any triangulation of that set? Similar bounds in higher dimensions are also given.
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