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» The Number of Triangulations on Planar Point Sets
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IPCO
2007
114views Optimization» more  IPCO 2007»
13 years 11 months ago
Distinct Triangle Areas in a Planar Point Set
Erd˝os, Purdy, and Straus conjectured that the number of distinct (nonzero) areas of the triangles determined by n noncollinear points in the plane is at least n−1 2 , which is...
Adrian Dumitrescu, Csaba D. Tóth
SODA
2004
ACM
115views Algorithms» more  SODA 2004»
13 years 11 months ago
Minimizing the stabbing number of matchings, trees, and triangulations
The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. We investigate probl...
Sándor P. Fekete, Marco E. Lübbecke, H...
ENDM
2008
118views more  ENDM 2008»
13 years 10 months ago
Number of Crossing-Free Geometric Graphs vs. Triangulations
We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...
Andreas Razen, Jack Snoeyink, Emo Welzl
SODA
2008
ACM
118views Algorithms» more  SODA 2008»
13 years 11 months ago
Geodesic Delaunay triangulation and witness complex in the plane
We introduce a new feature size for bounded domains in the plane endowed with an intrinsic metric. Given a point x in a domain X, the homotopy feature size of X at x measures half...
Jie Gao, Leonidas J. Guibas, Steve Oudot, Yue Wang
CCCG
2006
13 years 11 months ago
An O(n log n) Algorithm for the All-Farthest-Segments Problem for a Planar Set of Points
In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n log n) algorithm for th...
Asish Mukhopadhyay, Robert L. Scot Drysdale