Compression for 2-parameter persistent homology

Efficient two-parameter persistence computation via cohomology

“…We find that in our experiments, our method generally performs better without this preprocessing. In contrast, we observe that the preprocessing is very helpful for the the approach of [34,31], as previously reported [22]. We also observe that applying the chunk algorithm on cochain complexes instead of chain complexes may significantly increase the performance even for homology computation.…”

“…We have implemented our approach [32] and report timing results from computational experiments with function-Rips bifiltrations. On most instances considered, our approach is significantly faster than the approach [22] used in mpfree, and on certain instances, our implementation is able to outperform the approach of by a factor of up to 20.…”

“…A number of recent methods for computation of multiparameter persistence focus on decreasing the size of the input complex without changing its homology [21,41,22,2]. These methods can be used as a preprocessing step to the computation of a minimal free resolution.…”

“…These methods can be used as a preprocessing step to the computation of a minimal free resolution. In our computational experiments, we explore the effect of the chunk preprocessing method of [22] on the efficiency of our method. We find that in our experiments, our method generally performs better without this preprocessing.…”

“…While a resolution contains more information than a presentation, the underlying algorithmic problems are essentially the same, and we focus on the computation of a mfr in this work. Such a resolution is often quite small in practice [22], and computing it is a natural first step in computing invariants or metrics in the multi-parameter setting [12].…”