We propose novel algorithms for generating cofaces in the Vietoris-Rips complex. Cofaces -- simplices that contain a given simplex -- have multiple important uses in generating and using a Vietoris-Rips filtered complex: both in creating the coboundary matrix for computing cohomology, and as a more recent approach for generating the simplex stream in the first place. Traditionally, most methods have generated simplices first, and then sorted them in filtration order after the generation step. In this paper, we propose generating simplex streams by generating non-expanding cofaces, which by construction produces simplices in filtration order, and we propose generating additional cofaces in filtration order using sorted neighborhood lists to produce coboundaries directly in filtration order.

翻译：我们提出了在Vietoris-Rips复形中生成共面的新算法。共面——即包含给定单形的单形——在生成和使用Vietoris-Rips滤复形中具有多重重要用途：既可用于创建计算上同调的共边界矩阵，也可作为生成单形流的新近方法。传统上，多数方法首先生成单形，随后在生成步骤后按滤序进行排序。本文提出通过生成非扩张共面来生成单形流，该方法在构造过程中直接按滤序生成单形，并利用排序邻域列表按滤序生成附加共面，从而直接按滤序生成共边界。