Improved Stretch Factor of Delaunay Triangulations of Points in Convex Position

2019 ◽  
pp. 473-484 ◽  
Author(s):  
Xuehou Tan ◽  
Charatsanyakul Sakthip ◽  
Bo Jiang
Keyword(s):  
Delaunay Triangulations ◽  
Stretch Factor ◽  
Convex Position

scholarly journals On the stretch factor of Delaunay triangulations of points in convex position

2011 ◽  
Vol 44 (2) ◽  
pp. 104-109 ◽  
Author(s):  
Shiliang Cui ◽  
Iyad A. Kanj ◽  
Ge Xia
Keyword(s):  
Delaunay Triangulations ◽  
Stretch Factor ◽  
Convex Position

The Stretch Factor of L 1- and L  ∞ -Delaunay Triangulations

2012 ◽  
pp. 205-216 ◽  
Author(s):  
Nicolas Bonichon ◽  
Cyril Gavoille ◽  
Nicolas Hanusse ◽  
Ljubomir Perković
Keyword(s):  
Delaunay Triangulations ◽  
Stretch Factor

scholarly journals Almost all Delaunay triangulations have stretch factor greater than π/2

2011 ◽  
Vol 44 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Prosenjit Bose ◽  
Luc Devroye ◽  
Maarten Löffler ◽  
Jack Snoeyink ◽  
Vishal Verma
Keyword(s):  
Delaunay Triangulations ◽  
Stretch Factor ◽  
Almost All

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

scholarly journals Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral Triangles

2015 ◽  
Vol 44 (6) ◽  
pp. 1626-1649 ◽  
Author(s):  
Prosenjit Bose ◽  
Rolf Fagerberg ◽  
André van Renssen ◽  
Sander Verdonschot
Keyword(s):  
Delaunay Triangulations ◽  
Equilateral Triangles ◽  
Local Routing
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