Dynamic near-linear ε-additive Steiner spanners in hyperbolic space and removal of α(n) factor

Develop dynamic ε-additive Steiner spanners for n points in d-dimensional hyperbolic space H^d with near-linear edge count and efficient update time, and eliminate the α(n) factor appearing in current edge bounds (e.g., O_{ε,d}(n·log α(n))).

Background

The paper gives an ε-additive Steiner spanner in H^d with edge count close to linear, but the construction is static and carries a dependence on the inverse Ackermann function via transitive closure spanners. The authors highlight the desirability of dynamic maintenance for such additive spanners.

They explicitly pose achieving near-linear size in the dynamic setting and removing the α(n) dependence as open problems, pointing to potential algorithmic and geometric advances required to meet both goals.