The theory of the tight span, a cell complex that can be associated to every
metric $D$, offers a unifying view on existing approaches for analyzing
distance data, in particular for decomposing a metric $D$ into a sum of simpler
metrics as well as for representing it by certain specific edge-weighted
graphs, often referred to as realizations of $D$. Many of these approaches
involve the explicit or implicit computation of the so-called cutpoints of (the
tight span of) $D$, such as the algorithm for computing the "building blocks"
of optimal realizations of $D$ recently presented by A.