[lmcinnes]

For suitable specialized cases thins can be quite efficient. For persistent H_0 of VR-complexes in low-dimensional space there is an O(N log(N)) algorithm for N data points; that's decently fast. If you want H_1 I believe (but cannot prove) that there exists an O(N^2 log(N)) algorithm. Beyond H_1 things get painful. Since most PH software is written for general cases they don't tend to avail themselves of these special case shortcuts. Given that H_0 and H_1 of VR-complexes of low dimensional data covers a vast amount of the use cases I think specialized code for this would be worthwhile.