# On Euclidean Steiner $(1+\epsilon)$-Spanners

@article{Bhore2020OnES, title={On Euclidean Steiner \$(1+\epsilon)\$-Spanners}, author={Sujoy Bhore and Csaba D. T'oth}, journal={arXiv: Computational Geometry}, year={2020} }

Lightness and sparsity are two natural parameters for Euclidean $(1+\epsilon)$-spanners. Classical results show that, when the dimension $d\in \mathbb{N}$ and $\epsilon>0$ are constant, every set $S$ of $n$ points in $d$-space admits an $(1+\epsilon)$-spanners with $O(n)$ edges and weight proportional to that of the Euclidean MST of $S$. Tight bounds on the dependence on $\epsilon>0$ for constant $d\in \mathbb{N}$ have been established only recently. Le and Solomon (FOCS 2019) showed that…

## One Citation

### Light Euclidean Steiner Spanners in the Plane

- Mathematics, Computer ScienceSoCG
- 2021

For every finite set of points in the plane and every $\varepsilon>0$ there exists a Euclidean Steiner-spanner of lightness, and this matches the lower bound for $d=2$.

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