Constructing Efficient Non-Steiner Tree Covers and Spanners for Planar Domains

The paper presents efficient constructions of non-Steiner tree covers and spanners for planar domains, including polygonal domains, polyhedral terrains, and planar metrics. It identifies a surprising threshold phenomenon around stretch 2, where the number of trees in the non-Steiner tree cover transitions sharply. The paper also provides improved constructions of Steiner spanners for planar domains.