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arXiv · 2606.00245

Towards fast computation of higher discrete homology

Jacob Ender·Chris Kapulkin
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Abstract

We develop a new algorithm for computing the second discrete homology group of a graph which is much faster when compared to existing algorithms. To do so, we identify five basic shapes, which are quotient graphs of the 3-cube with the property that the injective maps from them detect all possible 2-boundaries in the singular chain complex computing discrete homology.

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Jacob Ender, Chris Kapulkin. 2026-05-29. Towards fast computation of higher discrete homology. https://arxiv.org/abs/2606.00245

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