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.

翻译：本文提出了一种在特征为零的域上计算图的离散立方同调的快速算法。相较于现有文献中的构造方法，本算法在多个计算步骤上实现了改进，其核心创新点包括：提出生成所有奇异立方体的更快速方法、通过模去立方体自同构群来降低链复形中向量空间的维数，以及利用离散立方同调的公理化处理对图进行预处理。