@inproceedings{Barba2014NewAI,
title={New and Improved Spanning Ratios for Yao Graphs},
author={L. Barba and P. Bose and M. Damian and R. Fagerberg and Wah Loon Keng and J. O’Rourke and Andr{\'e} van Renssen and Perouz Taslakian and S. Verdonschot and Ge Xia},
booktitle={Symposium on Computational Geometry},
year={2014}
}

For a set of points in the plane and a fixed integer k > 0, the Yao graph Yk partitions the space around each point into k equiangular cones of angle &thetas; = 2π/k, and connects each point to a nearest neighbor in each cone. It is known for all Yao graphs, with the sole exception of Y5, whether or not they are geometric spanners. In this paper we close this gap by showing that for odd k ≥ 5, the spanning ratio of Yk is at most 1/(1−2sin(3&thetas;/8)), which gives the first constant upper… CONTINUE READING