With the growing availability of efficient tools, persistent homology is becoming a useful methodology in a variety of applications. Significant work has been devoted to implementing tools for persistent homology diagrams; however, computing representative cycles corresponding to each point in the diagram can still be inefficient. To circumvent this problem, we extend the twist algorithm of Chen and Kerber. Our extension is based on a new technique we call saving, which supplements their existing killing technique. The resulting two-pass strategy can be realized using an existing matrix reduction implementation as a black-box and improves the efficiency of computing representatives of persistent homology generators. We prove the correctness of the new approach and experimentally show its performance.

翻译：随着高效工具的日益普及，持久同调正成为各类应用中的实用方法。尽管已有大量工作致力于实现持久同调图工具，但计算图中每个点对应的代表环仍可能效率低下。为解决此问题，我们扩展了Chen和Kerber的扭曲算法。该扩展基于我们称之为"保存"的新技术，作为其原有"杀死"技术的补充。由此产生的两趟策略可利用现有矩阵约简实现作为黑盒模块，从而提升持久同调生成元代表元的计算效率。我们证明了新方法的正确性，并通过实验展示了其性能表现。