Computer Science – Computational Geometry
Scientific paper
2011-03-22
Computer Science
Computational Geometry
36 pages, 6 figures, a preliminary version of this paper will appear in the Proceedings of the 27th Annual Symposium on Comput
Scientific paper
Let $S$ be a finite set of points in the Euclidean plane. Let $D$ be a Delaunay triangulation of $S$. The {\em stretch factor} (also known as {\em dilation} or {\em spanning ratio}) of $D$ is the maximum ratio, among all points $p$ and $q$ in $S$, of the shortest path distance from $p$ to $q$ in $D$ over the Euclidean distance $||pq||$. Proving a tight bound on the stretch factor of the Delaunay triangulation has been a long standing open problem in computational geometry. In this paper we prove that the stretch factor of the Delaunay triangulation of a set of points in the plane is less than $\rho = 1.998$, improving the previous best upper bound of 2.42 by Keil and Gutwin (1989). Our bound 1.998 is better than the current upper bound of 2.33 for the special case when the point set is in convex position by Cui, Kanj and Xia (2009). This upper bound breaks the barrier 2, which is significant because previously no family of plane graphs was known to have a stretch factor guaranteed to be less than 2 on any set of points.
No associations
LandOfFree
The Stretch Factor of the Delaunay Triangulation Is Less Than 1.998 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Stretch Factor of the Delaunay Triangulation Is Less Than 1.998, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Stretch Factor of the Delaunay Triangulation Is Less Than 1.998 will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-49705