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Multi-parameter persistent homology naturally arises in applications ofpersistent topology to data that come with extra information depending onadditional parameters, like for example time series data. We introduce theconcept of a Vietoris-Rips transformation, a method that reduces thecomputation of the one-parameter persistent homology of pathwise subcomplexesin multi-filtered flag complexes to the computation of the Vietoris-Ripspersistent homology of certain semimetric spaces. The corresponding pathwisepersistence barcodes track persistence features of the ambient multi-filteredcomplex and can in particular be used to recover the rank invariant inmulti-parameter persistent homology. We present MuRiT, a scalable algorithmthat computes the pathwise persistence barcodes of multi-filtered flagcomplexes by means of Vietoris-Rips transformations. Moreover, we provide anefficient software implementation of the MuRiT algorithm which resorts toRipser for the actual computation of Vietoris-Rips persistence barcodes. Todemonstrate the applicability of MuRiT to real-world datasets, we establishMuRiT as part of our CoVtRec pipeline for the surveillance of the convergentevolution of the coronavirus SARS-CoV-2 in the current COVID-19 pandemic.

MuRiT: Efficient Computation of Pathwise Persistence Barcodes in Multi-Filtered Flag Complexes via Vietoris-Rips Transformations