Distributed Persistent Homology for 2D Alpha Complexes

  • Freya Jensen (University of Heidelberg)
E2 10 (Leon-Lichtenstein)


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.

Antje Vandenberg

MPI for Mathematics in the Sciences Contact via Mail

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