  The paper introduces a special case of the Euclidean distance matrix
completion problem (edmcp) of interest in statistical data analysis where only
the minimal spanning tree distances are given and the matrix completion must
preserve the minimal spanning tree. Two solutions are proposed, one an
adaptation of a more general method based on a dissimilarity parameterized
formulation, the other an entirely novel method which constructs the point
configuration directly through a guided random search. These methods as well as
three standard edcmp methods are described and compared experimentally on real
and synthetic data. It is found that the constructive method given by the
guided random search algorithm clearly outperforms all others considered here.
Notably, standard methods including the adaptation force peculiar, and
generally unwanted, geometric structure on the point configurations their
completions produce.
