Filtration simplification for persistent homology via edge contraction (Q2203349)

The authors are interested in the natural problem to contract edges in complexes in the initial sequence to obtain a sequence of simplified complexes while controlling the perturbation between the original and simplified persistence diagrams. This paper is an extended version of a precedent work the same authors where they developed two contraction operators for the case where the initial sequence is a filtration [\textit{T. K. Dey} and \textit{R. Slechta}, Lect. Notes Comput. Sci. 11414, 89--100 (2019; Zbl 1486.55012)]. Here, they present proofs relevant to the filtration case and develop contraction operators for towers and multiparameter filtrations.