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arXiv · 1903.06064

On polynomial-time solvable linear Diophantine problems

Iskander Aliev
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Abstract

We obtain a polynomial-time algorithm that, given input (A, b), where A=(B|N) is an integer mxn matrix, m<n, with nonsingular mxm submatrix B and b is an m-dimensional integer vector, finds a nonnegative integer solution to the system Ax=b or determines that no such solution exists, provided that b is located sufficiently "deep" in the cone generated by the columns of B. This result improves on some of the previously known conditions that guarantee polynomial-time solvability of linear Diophantine problems.

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Iskander Aliev. 2020-04-02. On polynomial-time solvable linear Diophantine problems. https://doi.org/10.2140/moscow.2019.8.357

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