There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Competitive online routing in geometric graphs
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
Delaunay graphs are almost as good as complete graphs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
On the Stretch Factor of Convex Delaunay Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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
Competitive routing in the half-θ6-graph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the stretch factor of the theta-4 graph
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
| Hi-index | 0.00 |
In this paper we determine the stretch factor of L1-Delaunay and L∞-Delaunay triangulations, and we show that it is equal to $\sqrt{4+2\sqrt{2}} \approx 2.61$. Between any two points x,y of such triangulations, we construct a path whose length is no more than $\sqrt{4+2\sqrt{2}}$ times the Euclidean distance between x and y, and this bound is the best possible. This definitively improves the 25-year old bound of $\sqrt{10}$ by Chew (SoCG '86). This is the first time the stretch factor of the Lp-Delaunay triangulations, for any real p≥1, is determined exactly.