Euclidean Steiner Shallow-Light Trees in Higher Dimensions

Abstract

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.