Towards fast computation of higher discrete homology
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866913174832283648 |
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| author | Ender, Jacob Kapulkin, Chris |
| author_facet | Ender, Jacob Kapulkin, Chris |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards fast computation of higher discrete homology Ender, Jacob Kapulkin, Chris Computational Geometry Algebraic Topology Combinatorics 05-04 (primary), 05C25, 55U15 (secondary) 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. |
| title | Towards fast computation of higher discrete homology |
| topic | Computational Geometry Algebraic Topology Combinatorics 05-04 (primary), 05C25, 55U15 (secondary) |
| url | https://arxiv.org/abs/2606.00245 |