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.  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 3/7 n + 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.
|Number of pages||4|
|State||Published - 2007|
|Event||19th Annual Canadian Conference on Computational Geometry, CCCG 2007 - Ottawa, ON, Canada|
Duration: 20 Aug 2007 → 22 Aug 2007
|Conference||19th Annual Canadian Conference on Computational Geometry, CCCG 2007|
|Period||20/08/07 → 22/08/07|
Bibliographical noteFunding Information:
E-mail addresses: email@example.com (E. Ackerman), firstname.lastname@example.org (O. Aichholzer), email@example.com (B. Keszegh). 1 Supported by the Austrian FWF Joint Research Project ‘Industrial Geometry’ S9205-N12. 2 This work was done while visiting the School of Computing Science at Simon Fraser University.
ASJC Scopus subject areas
- Geometry and Topology