Improved Upper Bounds on the Reflexivity of Point Sets
نویسندگان
چکیده
Given a set S of n points in the plane, the reflexivity of S, ρ(S), is the minimum number of reflex vertices in a simple polygonalization of S. Arkin et al. [4] proved that ρ(S) ≤ ⌈n/2⌉ for any set S, and conjectured that the tight upper bound is ⌊n/4⌋. We show that the reflexivity of any set of n points is at most 3 7n+ O(1) ≈ 0.4286n. Using computer-aided abstract order type extension the upper bound can be further improved to 5 12n+O(1) ≈ 0.4167n.
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عنوان ژورنال:
- Comput. Geom.
دوره 42 شماره
صفحات -
تاریخ انتشار 2007