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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.16562 |
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| _version_ | 1866914068479082496 |
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| author | Lohrey, Markus Rosowski, Andreas |
| author_facet | Lohrey, Markus Rosowski, Andreas |
| contents | We study the parameterized complexity of the following factorization problem: given elements $a,a_1, \ldots, a_m$ of a monoid and a parameter $k$, can $a$ be written as the product of at most (or exactly) $k$ elements from $a_1, \ldots, a_m$. Several new upper bounds and fpt-equivalences with more restricted problems (subset sum and knapsack) are shown. Finally, some new upper bounds for variants of the parameterized change-making problems are shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16562 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parameterized Complexity of Factorization Problems Lohrey, Markus Rosowski, Andreas Group Theory 20B05, 20F10, 68Q45 We study the parameterized complexity of the following factorization problem: given elements $a,a_1, \ldots, a_m$ of a monoid and a parameter $k$, can $a$ be written as the product of at most (or exactly) $k$ elements from $a_1, \ldots, a_m$. Several new upper bounds and fpt-equivalences with more restricted problems (subset sum and knapsack) are shown. Finally, some new upper bounds for variants of the parameterized change-making problems are shown. |
| title | Parameterized Complexity of Factorization Problems |
| topic | Group Theory 20B05, 20F10, 68Q45 |
| url | https://arxiv.org/abs/2311.16562 |