Discrete & Computational Geometry

, Volume 50, Issue 2, pp 330–353

Morse Theory for Filtrations and Efficient Computation of Persistent Homology


  • Konstantin Mischaikow
    • Department of Mathematics and BioMaPSRutgers, The State University of New Jersey
    • Department of MathematicsThe University of Pennsylvania

DOI: 10.1007/s00454-013-9529-6

Cite this article as:
Mischaikow, K. & Nanda, V. Discrete Comput Geom (2013) 50: 330. doi:10.1007/s00454-013-9529-6


We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations.


Computational topologyDiscrete Morse theoryPersistent homology

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© Springer Science+Business Media New York 2013