Distributed Persistent Homology for 2D Alpha Complexes

I will introduce a new algorithm to parallelise the computation of persistent homology of 2D alpha complexes. The algorithm distributes the input point cloud among the cores which then compute a cover based on a rectilinear grid. I will show how to compute the persistence Mayer–Vietoris spectral sequence from these covers and how to obtain persistent homology from it. For this, I introduce second-page collapse conditions and explain how to solve the extension problem. I will give a short overview of an implementation in C++ using Open MPI and discuss some experimental results. Finally, I will give an outlook on the three-dimensional case and some applications.