Improved Spanning on Theta-5

Abstract

We show an upper bound of $\frac{\sin \left(\frac{3\pi }{10}\right)}{\sin \left(\frac{2\pi }{5}\right)-\sin \left(\frac{3\pi }{10}\right)}<5.70$ on the spanning ratio of ${\Theta }_5$-graphs, improving on the previous best known upper bound of $9.96$ [Bose, Morin, van Renssen, and Verdonschot. The Theta-5-graph is a spanner. Computational Geometry, 2015.]

21 pages, 30 figures, to be published in the proceedings of WADS 2021, The 17th Algorithms and Data Structures Symposium