  Today, very large amounts of data are produced and stored in all branches of
society including science. Mining these data meaningfully has become a
considerable challenge and is of the broadest possible interest. The size, both
in numbers of observations and dimensionality thereof, requires data mining
algorithms to possess time complexities with both variables that are linear or
nearly linear. One such algorithm, see Comput. Phys. Commun. 184, 2446-2453
(2013), arranges observations into a sequence called the progress index. The
progress index steps through distinct regions of high sampling density
sequentially. By means of suitable annotations, it allows a compact
representation of the behavior of complex systems, which is encoded in the
original data set. The only essential parameter is a notion of distance between
observations. Here, we present the shared memory parallelization of the key
step in constructing the progress index, which is the calculation of an
approximation of the minimum spanning tree of the complete graph of
observations. We demonstrate that excellent parallel efficiencies are obtained
for up to 72 logical (CPU) cores. In addition, we introduce three conceptual
advances to the algorithm that improve its controllability and the
interpretability of the progress index itself.
