# Faster computations of discrete homology

arXiv: https://arxiv.org/abs/2410.09939 · HTML: https://mlsanity.com/paper/2410.09939/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2024.

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

- [Topological data analysis using persistent discrete homology](https://mlsanity.com/paper/2506.15020/) (2025)

## Abstract (arXiv)

Machine computation of the discrete homology of graphs has stopped at degree two. We present an algorithm that reaches degree four. It generates the singular cubes inductively, pairing cubes one degree down instead of filtering all set maps; quotients the chain modules by the hyperoctahedral group action, over a field of sufficiently large characteristic; and shrinks the graph beforehand using homotopy invariance. The fourth homology group of the five-cycle, previously beyond the reach of machine computation, is computed in under two days.