Abstract

Computation of the interleaving distance between persistence modules is a central task in topo- logical data analysis. For 1-D persistence modules, thanks to the isometry theorem, this can be done by computing the bottleneck distance with known efficient algorithms. The question is open for most n-D persistence modules, n > 1, because of the well recognized complications of the indecomposables. Here, we consider a reasonably complicated class called 2-D interval decom- posable modules whose indecomposables may have a description of non-constant complexity. We present a polynomial time algorithm to compute the bottleneck distance for these modules from indecomposables, which bounds the interleaving distance from above, and give another algorithm to compute a new distance called dimension distance that bounds it from below

Paper