English

Improved Spanning on Theta-5

Computational Geometry 2021-06-03 v1

Abstract

We show an upper bound of sin(3π10)sin(2π5)sin(3π10)<5.70\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 Θ5\Theta_5-graphs, improving on the previous best known upper bound of 9.969.96 [Bose, Morin, van Renssen, and Verdonschot. The Theta-5-graph is a spanner. Computational Geometry, 2015.]

Cite

@article{arxiv.2106.01236,
  title  = {Improved Spanning on Theta-5},
  author = {Prosenjit Bose and Darryl Hill and Aurélien Ooms},
  journal= {arXiv preprint arXiv:2106.01236},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-24T02:45:21.347Z