I am interested in the topic of persistent homology (topological data analysis). According to what I read, there is some roadblock in the analysis of "big data" using persistent homology as it is considered rather computationally intensive. Computation of the simplicial complexes of a large point cloud often relies on extracting a sample. For example we use a witness complex.
My main question is, what is the current maximum or upper bound on the number of points in the point cloud for computing persistent homology?
Or in other words, what is the "world-record" in the number of points allowed by state-of-the-art persistent homology algorithms? Is it in the range of thousands of points, or millions of points?