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PreprintarXiv licencearXiv

RedZeD: Computing persistent homology by Reduction to Zero Differentials

  • Chris Kapulkin
  • Nathan Kershaw
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Abstract

We introduce a new algorithm for computing persistent homology of Vietoris-Rips filtrations, which offers a considerable improvement both in terms of time and memory over the existing implementations of the persistence pairing algorithm. The key innovation, called active enumeration, is made possible by a new theoretical framework of Reduction to Zero Differentials (hence RedZeD) in which to view persistent homology.

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Cite

BibTeXRIS
BibTeX
@misc{kapulkin2026redzed,
  title = {{RedZeD: Computing persistent homology by Reduction to Zero Differentials}},
  author = {Chris Kapulkin and Nathan Kershaw},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.06310},
  eprint = {2606.06310},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.06310},
}
RIS
TY  - UNPB
TI  - RedZeD: Computing persistent homology by Reduction to Zero Differentials
AU  - Chris Kapulkin
AU  - Nathan Kershaw
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2606.06310
UR  - https://arxiv.org/abs/2606.06310
AB  - We introduce a new algorithm for computing persistent homology of Vietoris-Rips filtrations, which offers a considerable improvement both in terms of time and memory over the existing implementations of the persistence pairing algorithm. The key innovation, called active enumeration, is made possible by a new theoretical framework of Reduction to Zero Differentials (hence RedZeD) in which to view persistent homology.
ER  -