Projects per year
Abstract
We extend the (recently introduced) notion of kconvexity of a twodimensional subset of the Euclidean plane to finite point sets. A set of n points is considered kconvex 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 npoint set contains a subset of Ω(log2 n) points that are in 2convex position. This bound is asymptotically tight. From an algorithmic point of view, we show that 2convexity of a finite point set can be decided in polynomial time, whereas the corresponding problem on kconvexity becomes NPcomplete for any fixed k ≥ 3
Original language  English 

Pages (fromto)  809832 
Journal  Computational Geometry: Theory and Applications 
Volume  47 
Issue number  8 
DOIs  
Publication status  Published  2014 
Fields of Expertise
 Information, Communication & Computing
Treatment code (Nähere Zuordnung)
 Theoretical
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Discrete and Computational Geometry
Hackl, T., Aigner, W., Pilz, A., Vogtenhuber, B., Kornberger, B. & Aichholzer, O.
1/01/05 → …
Project: Research area

FWF  ComPoSe  EuroGIAG_ErdösSzekeres type problems for colored point sets and compatible graphs
1/10/11 → 31/12/15
Project: Research project

FWF  CPGG  Combinatorial Problems on Geometric Graphs
Hackl, T.
1/09/11 → 31/12/15
Project: Research project