Computation of the interleaving distance between persistence modules is a central task in topological 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 {\em 2-D interval decomposable} 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 {\em dimension distance} that bounds it from below  .
Computation of the interleaving distance between persistence modules is a central task in topological data analysis. For 1-parameter 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-parameter persistence modules, n>1, because of the well recognized complications of the indecomposables. Here, we consider a reasonably complicated class called {\em n-parameter interval decomposable} 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 {\em dimension distance} that bounds it from below . An earlier version of this paper considered only the 2-parameter interval decomposable modules~\mbox{%DIFAUXCMD DeyCheng18 .
R
1-D
1-parameter
R
n-D
n-parameter
R
2-D
n-parameter
A
. An earlier version of this paper considered only the 2-parameter interval decomposable modules~\mbox{%DIFAUXCMD DeyCheng18