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Abstract
We extend the (recently introduced) notion of k-convexity of a two-dimensional subset of the Euclidean plane to finite point sets. A set of n points is considered k-convex if there exists a spanning (simple) polygonization such that the intersection of any straight line with its interior consists of at most k disjoint intervals. As the main combinatorial result, we show that every n-point set contains a subset of Ω(log2 n) points that are in 2-convex position. This bound is asymptotically tight. From an algorithmic point of view, we show that 2-convexity of a finite point set can be decided in polynomial time, whereas the corresponding problem on k-convexity becomes NP-complete for any fixed k ≥ 3
Originalsprache | englisch |
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Seiten (von - bis) | 809-832 |
Fachzeitschrift | Computational Geometry: Theory and Applications |
Jahrgang | 47 |
Ausgabenummer | 8 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2014 |
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Theoretical
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