Efficient computations of discrete cubical homology

We present a fast algorithm for computing discrete cubical homology of graphs over a field of characteristic zero. This algorithm improves on several computational steps compared to constructions in the existing literature, with the key insights including: a faster way to generate all singular cubes, reducing the dimensions of vector spaces in the chain complex by taking a quotient over automorphisms of the cube, and preprocessing graphs using the axiomatic treatment of discrete cubical homology.