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.

翻译：我们提出了一种用于计算Vietoris–Rips滤流的持续同调的新算法，该算法在许多情况下相比现有持续配对算法实现具有显著的加速效果。其关键创新——称为主动枚举——得益于一个名为"归约至零微分"（RedZeD）的新理论框架，该框架为理解持续同调提供了新的视角。