This paper proves a conjecture by Solomon about Steiner shallow-light trees (SLT) in Euclidean $d$-space: It is shown that for any finite point set $\mathbb{R}^d$, any root, and any $ε>0$, there is a Euclidean Steiner $(1+ε,O(\sqrt{1/ε}))$-SLT without any dependence on dimension. We also revisit the core example, designed by Solomon, in the plane and its generalization to $d$-space.

翻译：本文证明了Solomon关于欧几里得$d$维空间中斯坦纳浅光树（Steiner shallow-light tree, SLT）的一个猜想：对于$\mathbb{R}^d$中任意有限点集、任意根节点及任意$ε>0$，存在一个与维度无关的欧几里得斯坦纳$(1+ε,O(\sqrt{1/ε}))$-SLT。我们还重新审视了Solomon在平面上设计的核心例子及其在$d$维空间中的推广。