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.