Benchmark data sets of minimal presentations of 2-parameter persistence modules

The repository contains a large collection of minimal presentations in scc2020 format (defined here) for various common bifiltrations in multi-parameter persistent homology. Specifically, it contains the minimal presentations of the datasets 

• from the mpfree benchmark dataset (see https://doi.org/10.3217/xcs8c-hjm53)
• from the Delaunay bifiltration project (see https://doi.org/10.1137/1.9781611977912.173)

Moreover, it provides some additional minimal presentations generated from a simple random process. For its description, see the paper

Tamal Dey, Jan Jendrysiak, Michael Kerber: Decomposing Multiparameter Persistence Modules, SoCG 2025

The naming convention of the files generally follows the pattern

[instance_type]_[instance_size]_[instance_number].scc_[dimension]

where the instance_size in most cases denotes the number of points in the bifiltration, and instance_number is between 1 and 5, as most instances are generated 5 times with different random seeds. "dimension" corresponds to the position in the initial chain complex on which the minimal presentation is computed. Unfortunately, this does not directly correspond to the homology dimension but it is reflected (because the scc2020 format is in decreasing order) For instance

S1_random_10000_3.scc_2

is the minimal presentation in homology dimension 0 for 10000 points sampled on the unit circle, and it is the third out of 5 such instances.

All presentation files are contained in the folder "instances". The folder "instances_small" contains a subset of the files for which benchmark files terminate much faster.

The file "README.txt" documents how the instances have been generated in more detail.