Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Approximating geometric bottleneck shortest paths
Computational Geometry: Theory and Applications
Geometric Spanner Networks
Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Undirected connectivity of sparse Yao graphs
FOMC '11 Proceedings of the 7th ACM ACM SIGACT/SIGMOBILE International Workshop on Foundations of Mobile Computing
Computational Geometry: Theory and Applications
On certain geometric properties of the Yao---Yao graphs
Journal of Combinatorial Optimization
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The Yao and Theta graphs are defined for a given point set and a fixed integer k 0. The space around each point is divided into k cones of equal angle, and each point is connected to a nearest neighbor in each cone. The difference between Yao and Theta graphs is in the way the nearest neighbor is defined: Yao graphs minimize the Euclidean distance between a point and its neighbor, and Theta graphs minimize the Euclidean distance between a point and the orthogonal projection of its neighbor on the bisector of the hosting cone. We prove that, corresponding to each edge of the Theta graph Θ6, there is a path in the Yao graph Y6 whose length is at most 8.82 times the edge length. Combined with the result of Bonichon, Gavoille, Hanusse and Ilcinkas, who prove an upper bound of 2 on the stretch factor of Θ6, we obtain an upper bound of 17.7 on the stretch factor of Y6.