Clear and Compress: Computing Persistent Homology in Chunks

  • Ulrich Bauer
  • Michael Kerber
  • Jan Reininghaus
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.


Betti Number Cubical Complex Chunk Size Column Operation Boundary Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank Chao Chen, Herbert Edelsbrunner, and Hubert Wagner for helpful discussions. This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP and the Max Planck Center for Visual Computing and Communication.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ulrich Bauer
    • 1
  • Michael Kerber
    • 2
    • 3
  • Jan Reininghaus
    • 1
  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria
  2. 2.Stanford UniversityStanfordUSA
  3. 3.Max-Planck-Institut für InformatikSaarbrückenGermany

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