  The first paper explored two strength indicators (extreme point ratio (EPR)
and centroid distance (CD)), both of which predict that subtours of the
spanning tree in hypergraph polytope STHGP having large cardinality are
significantly stronger than the corresponding subtours of small cardinality. In
this second paper, we exploit this previously unknown property algorithmically
within GeoSteiner, presenting strong computational evidence that the EPR and CD
indicators are highly predictive of actual computational strength, at least for
subtour inequalities of STHGP. The GeoSteiner package for geometric Steiner
trees in the plane uses STHGP to solve the Full Steiner Tree (FST)
concatenation problem. The separation algorithms in previous versions of
GeoSteiner find violated subtours of only relatively small cardinality, and we
examine the underlying algorithmic causes. We present improvements in
GeoSteiner specifically designed to strengthen violated subtours by
augmentation (instead of reduction), yielding violated subtours of large
cardinality. Across all distance metrics and instance classes studied, the
computational results are remarkable -- culminating with an optimal solution of
a 1,000,000 terminal random Euclidean instance. The conclusion is that the EPR
and CD strength indicators presented in the first paper have strong predictive
power regarding actual computational strength (at least regarding STHGP
subtours). The ability to accurately measure the strength of inequalities has
numerous applications of great importance, both in theory and practice.
