Euclidean Steiner Shallow-Light Trees in Higher Dimensions

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 $\epsilon >0$, there is a Euclidean Steiner $(1+\epsilon ,O(\sqrt{1\mathrm{/}\epsilon }))$-SLT without any dependence on dimension. We also revisit the core example, designed by Solomon, in the plane and its generalization to $d$-space.