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arXiv · 2606.06310

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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Chris Kapulkin, Nathan Kershaw. 2026-09-11. RedZeD: Computing persistent homology by Reduction to Zero Differentials. https://arxiv.org/abs/2606.06310

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