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math.OC2019
Optimizing Sparsity over Lattices and Semigroups
Iskander Aliev, Gennadiy Averkov, Jesús A. De Loera +1
Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero en…
math.NT2019
On polynomial-time solvable linear Diophantine problems
Iskander Aliev
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 vect…