  Different types of two- and three-dimensional representations of a finite
metric space are studied that focus on the accurate representation of the
linear order among the distances rather than their actual values. Lower and
upper bounds for representability probabilities are produced by experiments
including random generation, a rubber-band algorithm for accuracy optimization,
and automatic proof generation. It is proved that both farthest neighbour
representations and cluster tree representations always exist in the plane.
Moreover, a measure of order accuracy is introduced, and some lower bound on
the possible accuracy is proved using some clustering method and a result on
maximal cuts in graphs.
