| Prosenjit Bose 2 (2007) | |||||||||||||||
Abstract | |||||||||||||||
| Let K be a convex polytope in R d, let h(x) be the hyperplane consisting of all points with first coordinate equal to x, and let A(x) be the area (or volume, if d? 3) of the section K " h(x). Using the Brunn-Minkowski inequality, we show that A(x) is a strictly unimodal function and give an algorithm to determine a hyperplane that achieves the maximum. Our algorithm runs in linear time, if the facial lattice of K is given. 1 | |||||||||||||||
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