Self-adjusting binary search trees
Journal of the ACM (JACM)
Computational geometry: an introduction
Computational geometry: an introduction
Art gallery theorems and algorithms
Art gallery theorems and algorithms
The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n - 2
Discrete & Computational Geometry
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Fundamentals of restricted-orientation convexity
Information Sciences: an International Journal
An Optimal Algorithm for Finding the Kernel of a Polygon
Journal of the ACM (JACM)
Triangulation and shape-complexity
ACM Transactions on Graphics (TOG)
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
On Spanning Trees with Low Crossing Numbers
Data Structures and Efficient Algorithms, Final Report on the DFG Special Joint Initiative
Minimizing the stabbing number of matchings, trees, and triangulations
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A Note on Convex Decompositions of a Set of Points in the Plane
Graphs and Combinatorics
Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-Triangles
Graphs and Combinatorics
Coverage with k-transmitters in the presence of obstacles
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Art galleries, k-modems, and k-convexity
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
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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(nlogn) time. A description of their shape is given as well, which leads to Erdos-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.