Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Shortest paths in an arrangement with k line orientations
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Which Triangulations Approximate the Complete Graph?
Proceedings of the International Symposium on Optimal Algorithms
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
A fast algorithm for approximating the detour of a polygonal chain
Computational Geometry: Theory and Applications
Geometric Spanner Networks
Geometric dilation of closed planar curves: New lower bounds
Computational Geometry: Theory and Applications
On geometric dilation and halving chords
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
The density of iterated crossing points and a gap result for triangulations of finite point sets
Proceedings of the twenty-second annual symposium on Computational geometry
On the density of iterated line segment intersections
Computational Geometry: Theory and Applications
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Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on the circle, this question seems hard to answer; it is not even clear if there exists a lower bound 1. In this paper we provide the first upper and lower bounds for the embedding problem. Each finite point set can be embedded into the vertex set of a finite triangulation of dilation ≤ 1.1247. Each embedding of a closed convex curve has dilation ≥ 1.00157. Let P be the plane graph that results from intersecting n infinite families of equidistant, parallel lines in general position. Then the vertex set of P has dilation $\geq 2/\sqrt{3} \approx 1.1547$.