Compression for 2-parameter persistent homology

Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead large inputs, and tasks this area tend be expensive. We propose two methods for chain complexes free 2-parameter persistence modules. The first method extends multi-chunk algorithm one-parameter returning smallest complex among all ones quasi-isomorphic input. second produces minimal presentations homology input; it based on Lesnick Wright, but incorporates several improvements that substantial performance gains. are complementary, can combined compute with millions generators few seconds. have been implemented, software publicly available. report experimental evaluations, which demonstrate compared previously available strategies.