On polynomial-time solvable linear Diophantine problems
Number Theory
2020-04-03 v3 Combinatorics
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.
Cite
@article{arxiv.1903.06064,
title = {On polynomial-time solvable linear Diophantine problems},
author = {Iskander Aliev},
journal= {arXiv preprint arXiv:1903.06064},
year = {2020}
}
Comments
This is a generalisation and extension of the results from the previous version. At the time the previous version was written, the author was not aware of the results of Brimkov [5]