Computational geometry: an introduction
Computational geometry: an introduction
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
The Delauney Triangulation Closely Approximates the Complete Euclidean Graph
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Geometric Spanner Networks
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Delaunay graphs are almost as good as complete graphs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
On Spanners and Lightweight Spanners of Geometric Graphs
SIAM Journal on Computing
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
Almost all Delaunay triangulations have stretch factor greater than π/2
Computational Geometry: Theory and Applications
Improved upper bound on the stretch factor of delaunay triangulations
Proceedings of the twenty-seventh annual symposium on Computational geometry
| Hi-index | 0.00 |
Let S be a finite set of points in the Euclidean plane. Let G be a geometric graph in the plane whose point set is S. The stretch factor of G is the maximum ratio, among all points p and q in S, of the length of the shortest path from p to q in G over the Euclidean distance |pq|. Keil and Gutwin in 1989 [11] proved that the stretch factor of the Delaunay triangulation of a set of points S in the plane is at most 2@p/(3cos(@p/6))~2.42. Improving on this upper bound remains an intriguing open problem in computational geometry. In this paper we consider the special case when the points in S are in convex position. We prove that in this case the stretch factor of the Delaunay triangulation of S is at most @r=2.33.