Projects per year
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
Original language | English |
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Pages (from-to) | 809-832 |
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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Dive into the research topics of 'On k-convex point sets'. Together they form a unique fingerprint.Projects
- 3 Finished
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FWF - ComPoSe - EuroGIAG_Erdös-Szekeres type problems for colored point sets and compatible graphs
Aichholzer, O. (Principal Investigator (PI))
1/10/11 → 31/12/15
Project: Research project
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FWF - CPGG - Combinatorial Problems on Geometric Graphs
Hackl, T. (Principal Investigator (PI))
1/09/11 → 31/12/15
Project: Research project
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Discrete and Computational Geometry
Hackl, T. (Co-Investigator (CoI)), Aigner, W. (Co-Investigator (CoI)), Pilz, A. (Co-Investigator (CoI)), Vogtenhuber, B. (Co-Investigator (CoI)), Kornberger, B. (Co-Investigator (CoI)) & Aichholzer, O. (Co-Investigator (CoI))
1/01/05 → 31/12/24
Project: Research area