Abstract
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 3/7 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.
| Original language | English |
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| Pages | 29-32 |
| Number of pages | 4 |
| State | Published - 2007 |
| Externally published | Yes |
| Event | 19th Annual Canadian Conference on Computational Geometry, CCCG 2007 - Ottawa, ON, Canada Duration: 20 Aug 2007 → 22 Aug 2007 |
Conference
| Conference | 19th Annual Canadian Conference on Computational Geometry, CCCG 2007 |
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| Country/Territory | Canada |
| City | Ottawa, ON |
| Period | 20/08/07 → 22/08/07 |
Bibliographical note
Funding Information:E-mail addresses: [email protected] (E. Ackerman), [email protected] (O. Aichholzer), [email protected] (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