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Regular version of the site

Article

FPT-algorithms for some problems related to integer programming

Journal of Combinatorial Optimization. 2018. Vol. 35. No. 4. P. 1128-1146.

In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems’ formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms with respect to the same parameter for the problems, when the matrices have no singular rank submatrices.