Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Approximating geometric bottleneck shortest paths
Computational Geometry: Theory and Applications
Geometric Spanner Networks
Plane spanners of maximum degree six
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Almost all Delaunay triangulations have stretch factor greater than π/2
Computational Geometry: Theory and Applications
On Spanners and Lightweight Spanners of Geometric Graphs
SIAM Journal on Computing
Improved local algorithms for spanner construction
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Improved upper bound on the stretch factor of delaunay triangulations
Proceedings of the twenty-seventh annual symposium on Computational geometry
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Given a set P of n points in the plane, we show how to compute in O(nlogn) time a spanning subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong plane t-spanner of P with t=(1+2)^2@?@d, where @d is the spanning ratio of the Delaunay triangulation. Furthermore, the maximum degree bound can be reduced slightly to 6 while remaining a strong plane constant spanner at the cost of an increase in the spanning ratio and no longer being a subgraph of the Delaunay triangulation.