Upper bounds on geometric permutations for convex sets |
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Authors: | Rephael Wenger |
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Institution: | (1) School of Computer Science, McGill University, 805 Sherbrooke Street West, H3A 2K6 Montreal, Quebec, Canada |
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Abstract: | LetA be a family ofn pairwise disjoint compact convex sets inR
d. Let
. We show that the directed lines inR
d, d 3, can be partitioned into
sets such that any two directed lines in the same set which intersect anyAA generate the same ordering onA. The directed lines inR
2 can be partitioned into 12n such sets. This bounds the number of geometric permutations onA by 1/2
d
ford3 and by 6n ford=2. |
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Keywords: | |
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