Towards fast computation of higher discrete homology
arXiv:2606.002456.4h-index: 1
Predicted impact top 17% in CG · last 90 daysOriginality Incremental advance
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This work provides a more efficient computational tool for researchers studying discrete homology in graphs, though it is incremental in nature.
The paper presents a faster algorithm for computing the second discrete homology group of a graph by identifying five basic shapes that detect all 2-boundaries, achieving significant speed improvements over existing methods.
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.