Discrete & Computational Geometry

, Volume 50, Issue 2, pp 330–353

Morse Theory for Filtrations and Efficient Computation of Persistent Homology


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

Copyright information

© 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