RedZeD: Computing persistent homology by Reduction to Zero Differentials

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.

arXiv comment32 pages; comments welcome