@article {
author = {Bakhshesh, D. and Farshi, M.},
title = {A degree 3 plane 5.19-spanner for points in convex position},
journal = {Scientia Iranica},
volume = {28},
number = {6},
pages = {3324-3331},
year = {2021},
publisher = {Sharif University of Technology},
issn = {1026-3098},
eissn = {2345-3605},
doi = {10.24200/sci.2021.56576.4796},
abstract = {Let $S$ be a set of $n$ points in the plane that is in convex position. In this paper, using the well-known path-greedy spanner algorithm, we present an algorithm that constructs a plane $\frac{3+4\pi}{3}$-spanner $G$ of degree 3 on the point set $S$. Recently, Biniaz et al. ({\it Towards plane spanners of degree 3, Journal of Computational Geometry, 8 (1), 2017}) have proposed an algorithm that constructs a degree 3 plane $\frac{3+4\pi}{3}$-spanner $G'$ for $S$. We show that there is no upper bound with a constant factor on the total weight of $G'$, but the total weight of $G$ is asymptotically equal to the total weight of the minimum spanning tree of $S$.},
keywords = {Plane spanner,Stretch factor,greedy spanner,Computational geometry},
url = {https://scientiairanica.sharif.edu/article_22416.html},
eprint = {https://scientiairanica.sharif.edu/article_22416_4b0d15eb08ab41c714ba9aecec88cf3a.pdf}
}