Discrete & Computational Geometry

, Volume 50, Issue 2, pp 330-353

First online:

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

  • Konstantin MischaikowAffiliated withDepartment of Mathematics and BioMaPS, Rutgers, The State University of New Jersey
  • , Vidit NandaAffiliated withDepartment of Mathematics, The University of Pennsylvania Email author 

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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