Morse Theory for Filtrations and Efficient Computation of Persistent Homology

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)330-353
Number of pages24
JournalDiscrete and Computational Geometry
Volume50
Issue number2
DOIs
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Computational topology
  • Discrete Morse theory
  • Persistent homology

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