Suri's minimum Steiner star conjecture for max-sum matchings

Let $S$ be an even set of points in the plane, and let $\mathcal M$ be a max-sum matching of $S$. Define $t(S)$ as the minimum, over points $y$ in the plane, of $\sum_{x\in S}\|y-x\|$, the length of a minimum Steiner star on $S$. Suri's conjecture. The minimum Steiner star satisfies

$$t(S)\leq \frac{2}{\sqrt{3}}\;\operatorname{cost}(\mathcal M).$$

This conjecture arose in the study of communication networks and was the motivation for Fingerhut's conjecture. The paper's theorem proving Fingerhut's conjecture also confirms this bound.