  In this paper we focus on preprocessing for persistent homology computations.
We adapt some techniques which 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 method (introduced by Mrozek, Pilarczyk and
\.Zelazna).

Geometric Topology