A classical result in distance based tree-reconstruction characterizes when for a distance D on some finite set X there exist a uniquely determined dendrogram on X (essentially a rooted tree T = (V,E) with leaf set X and no degree two vertices but possibly the root and an edge weighting ω : E → R≥0) such that the distance D(T,ω) induced by (T,ω) on X is D. Moreover, algorithms that quickly reco...