Discrete & Computational Geometry

, Volume 50, Issue 2, pp 330–353 | Cite as

Morse Theory for Filtrations and Efficient Computation of Persistent Homology



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 topology Discrete Morse theory Persistent homology 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematics and BioMaPSRutgers, The State University of New JerseyPiscatawayUSA
  2. 2.Department of MathematicsThe University of PennsylvaniaPhiladelphiaUSA

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