A heuristic technique for decomposing multisets of non-negative integers according to the Minkowski sum

نویسندگان

چکیده

We study the following problem. Given a multiset $M$ of non-negative integers, decide whether there exist and, in positive case, compute two non-trivial multisets whose Minkowski sum is equal to $M$. The A and B containing all possible sums any element B. This problem was proved be NP-complete when are replaced by sets. version strictly related factorization boolean polynomials that turns out as well. When considered, equivalent with integer coefficients. computational complexity both these problems still unknown. main contribution this paper heuristic technique for decomposing integers. Experimental results show our decomposes hundreds elements within seconds independently magnitude numbers belonging multisets. Our can used also factoring N[x]. that, degree gets larger, much faster than state-of-the-art algorithms implemented commercial software like Mathematica MatLab.

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ژورنال

عنوان ژورنال: Discrete Mathematics & Theoretical Computer Science

سال: 2022

ISSN: ['1365-8050', '1462-7264']

DOI: https://doi.org/10.46298/dmtcs.9877