Minimal parametric networks in hyperspaces are nontrivial only in finiteness classes where all Hausdorff distances are finite, with interior vertices corresponding to Fermat-Steiner solutions and generalized conditions for one-sided distances on convex sets.
& Tuzhilin, A.: Fermat–Steiner problem in the metric space of compact sets endowed with Hausdorff distance
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Minimal Parametric Networks in Hyperspaces and their Properties
Minimal parametric networks in hyperspaces are nontrivial only in finiteness classes where all Hausdorff distances are finite, with interior vertices corresponding to Fermat-Steiner solutions and generalized conditions for one-sided distances on convex sets.