Parameterized Complexity of Factorization Problems

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 r...

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Bibliographic Details
Published inDiscrete Mathematics and Theoretical Computer Science Vol. 27:3; no. Discrete Algorithms; p. 1
Main Authors Lohrey, Markus, Rosowski, Andreas
Format Journal Article
LanguageEnglish
Published DMTCS 01.10.2025
Subjects
Algorithms
Mathematical research
Germany
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ISSN1365-8050
1462-7264
1365-8050
DOI10.46298/dmtcs.13087

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Summary: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.13087