This research analyzes factorization problems in monoids, revealing new relationships with subset sum and knapsack complexities.
We study the parameterized complexity of the following factorization problem: given elements a,a₁, …, aₘ of a monoid and a parameter k, can a be written as the product of at most (or exactly) k elements from a₁, …, aₘ. 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.
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Lohrey et al. (2025) studied this question.
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