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 log n ) 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
