On k-convex polygons
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Demaine_On k-convex.pdf
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Author(s)
Aichholzer, Oswin
Aurenhammer, Franz
Demaine, Erik D.
Hurtado, Ferran
Ramos, Pedro
Urrutia, Jorge
Date Issued
September 2011
Journal
Computational Geometry
Publisher
Elsevier
Citation
Aichholzer, Oswin, Franz Aurenhammer, Erik D. Demaine, Ferran Hurtado, Pedro Ramos, and Jorge Urrutia. “On k-Convex Polygons.” Computational Geometry 45, no. 3 (April 2012): 73–87.
Version
Original manuscript
Abstract
We introduce a notion of k -convexity and explore polygons in the plane that have this property. Polygons which are k -convex can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUM-hard problem. We give a characterization of 2-convex polygons, a particularly interesting class, and show how to recognize them in O(n logn) time. A description of their shape is given as well, which leads to Erdős–Szekeres type results regarding subconfigurations of their vertex sets. Finally, we introduce the concept of generalized geometric permutations, and show that their number can be exponential in the number of 2-convex objects considered.
Description
Original manuscript" July 21, 2010
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1016/j.comgeo.2011.09.001
