The maximum number of faces of the Minkowski sum of two convex polytopes
| Autor: | Karavelas, Menelaos I., Tzanaki, Eleni |
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| Rok vydání: | 2011 |
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| Druh dokumentu: | Working Paper |
| Popis: | We derive tight expressions for the maximum number of $k$-faces, $0\le{}k\le{}d-1$, of the Minkowski sum, $P_1\oplus{}P_2$, of two $d$-dimensional convex polytopes $P_1$ and $P_2$, as a function of the number of vertices of the polytopes. For even dimensions $d\ge{}2$, the maximum values are attained when $P_1$ and $P_2$ are cyclic $d$-polytopes with disjoint vertex sets. For odd dimensions $d\ge{}3$, the maximum values are attained when $P_1$ and $P_2$ are $\lfloor\frac{d}{2}\rfloor$-neighborly $d$-polytopes, whose vertex sets are chosen appropriately from two distinct $d$-dimensional moment-like curves. Comment: 37 pages, 8 figures, conference version to appear at SODA 2012; v2: fixed typos, made stylistic changes, added figures |
| Databáze: | arXiv |
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