• Corpus ID: 222142649

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

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

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