Extension to Doubling Spaces

Determine whether the techniques developed for minimum dilation trees in the Euclidean plane can be extended to doubling metric spaces without relying on Euclidean geometry.

Background

After raising the higher-dimensional extension, the paper identifies a broader possible generalization beyond Euclidean spaces. Specifically, it asks whether the techniques can be adapted to doubling spaces, which provide metric spaces with controlled geometric growth while omitting the Euclidean structure used throughout the paper.

References

Another natural extension, past higher-dimensional Euclidean spaces, is the question of whether these techniques can also be extended to doubling spaces, forgoing all Euclidean geometry.

— A Sublinear Approximation Algorithm for Minimum Dilation Trees in the Plane  (2609.08990 - Berg et al., 8 Sep 2026) in Section 7, Section “Conclusion”