Clear and Compress: Computing Persistent Homology in Chunks

Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

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.

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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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