# Computing Bottleneck Distance for Multi-parameter Interval Decomposable Persistence Modules

arXiv: https://arxiv.org/abs/1803.02869 · HTML: https://mlsanity.com/paper/1803.02869/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration](https://mlsanity.com/paper/2510.05102/) (2025)

## Abstract (arXiv)

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~citeDeyCheng18.