Euclidean Steiner Shallow-Light Trees in Higher Dimensions
arXiv:2605.2663328.9
Predicted impact top 41% in CG · last 90 daysOriginality Highly original
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Resolves a conjecture in geometric graph theory, providing dimension-independent bounds for shallow-light trees.
Proved Solomon's conjecture on Euclidean Steiner shallow-light trees, showing existence of a Steiner (1+ε, O(√(1/ε)))-SLT for any finite point set in ℝ^d with no dimension dependence.
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.