The Maximum Number of Faces of the Minkowski Sum of Two Convex Polytopes
نویسندگان
چکیده
منابع مشابه
The maximum number of faces of the Minkowski sum of two convex polytopes
We derive tight bounds for the maximum number of k-faces, 0 ≤ k ≤ d − 1, of the Minkowski sum, P1 ⊕ P2, of two ddimensional convex polytopes P1 and P2, as a function of the number of vertices of the polytopes. For even dimensions d ≥ 2, the maximum values are attained when P1 and P2 are cyclic d-polytopes with disjoint vertex sets. For odd dimensions d ≥ 3, the maximum values are attained when ...
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Consider a set of r convex d-polytopes P1, P2, . . . , Pr, where d ≥ 3 and r ≥ 2, and let ni be the number of vertices of Pi, 1 ≤ i ≤ r. It has been shown by Fukuda and Weibel [4] that the number of k-faces of the Minkowski sum, P1 + P2 + · · · + Pr, is bounded from above by Φk+r(n1, n2, . . . , nr), where Φl(n1, n2, . . . , nr) = ∑ 1≤si≤ni s1+...+sr=l ∏ r i=1 ( ni si ) , l ≥ r. Fukuda and Weib...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2015
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-015-9726-6