Simplification of complexes of persistent homology computations

Abstract

In this paper we focus on preprocessing for persistent homology computations. We adapt some techniques that were successfully used for standard homology computations. The main idea is to reduce the complex prior to generating its boundary matrix, which is costly to store and process. We discuss the following reduction methods: elementary collapses, coreductions (as defined by Mrozek and Batko), and acyclic subspace methods (introduced by Mrozek, Pilarczyk, and Żelazna).