RedZeD: Computing persistent homology by Reduction to Zero Differentials
This work addresses the computational bottleneck of persistent homology for Vietoris–Rips filtrations, offering a faster algorithm for researchers in topological data analysis.
The paper introduces RedZeD, a new algorithm for computing persistent homology of Vietoris–Rips filtrations that achieves considerable speedup over existing implementations by leveraging a new theoretical framework called Reduction to Zero Differentials.
We introduce a new algorithm for computing persistent homology of Vietoris--Rips filtrations, which in many cases offers a considerable speedup over the existing implementation 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.