Near-optimal dynamic Steiner spanners are constructed in all three constant-curvature geometries via a quadtree approach, and the hyperbolic-plane 2-spanner problem is settled at Θ(n log n) edges.
Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
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Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces
Near-optimal dynamic Steiner spanners are constructed in all three constant-curvature geometries via a quadtree approach, and the hyperbolic-plane 2-spanner problem is settled at Θ(n log n) edges.