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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20474 |
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| _version_ | 1866910546099437568 |
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| author | Barron, Thomas |
| author_facet | Barron, Thomas |
| contents | To the existing dynamic algorithm FactorizationsUpToElement for factorization sets of elements in a numerical semigroup, we add lexicographic and parallel behavior. To the existing parallel lexicographic algorithm for the same, we add dynamic behavior. The (dimensionwise) dynamic algorithm is parallelized either elementwise or factorizationwise, while the parallel lexicographic algorithm is made dynamic with low-dimension tabulation. The tabulation for the parallel lexicographic algorithm can itself be performed using the dynamic algorithm. We provide reference CUDA implementations with measured runtimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two parallel dynamic lexicographic algorithms for factorization sets in numerical semigroups Barron, Thomas Commutative Algebra Distributed, Parallel, and Cluster Computing Combinatorics 90C39, 68W10, 11-04 To the existing dynamic algorithm FactorizationsUpToElement for factorization sets of elements in a numerical semigroup, we add lexicographic and parallel behavior. To the existing parallel lexicographic algorithm for the same, we add dynamic behavior. The (dimensionwise) dynamic algorithm is parallelized either elementwise or factorizationwise, while the parallel lexicographic algorithm is made dynamic with low-dimension tabulation. The tabulation for the parallel lexicographic algorithm can itself be performed using the dynamic algorithm. We provide reference CUDA implementations with measured runtimes. |
| title | Two parallel dynamic lexicographic algorithms for factorization sets in numerical semigroups |
| topic | Commutative Algebra Distributed, Parallel, and Cluster Computing Combinatorics 90C39, 68W10, 11-04 |
| url | https://arxiv.org/abs/2407.20474 |