Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A fast algorithm for approximating the detour of a polygonal chain
Computational Geometry: Theory and Applications
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We design a fully polynomial-time approximation scheme for the problem of finding a triangulation of a simple polygon with a constant number of sources of dilation that achieves the minimum vertex dilation.