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» The Number of Triangulations on Planar Point Sets
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IPCO
2007
114views Optimization» more  IPCO 2007»
15 years 1 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»
15 years 1 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...
102
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ENDM
2008
118views more  ENDM 2008»
14 years 11 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»
15 years 1 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
15 years 1 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