FPT-algorithms for some problems related to integer programming

D. V. Gribanov (), D. S. Malyshev (), P. M. Pardalos () and S. I. Veselov ()
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D. V. Gribanov: Lobachevsky State University of Nizhny Novgorod
D. S. Malyshev: National Research University Higher School of Economics
P. M. Pardalos: National Research University Higher School of Economics
S. I. Veselov: Lobachevsky State University of Nizhny Novgorod

Journal of Combinatorial Optimization, 2018, vol. 35, issue 4, No 7, 1128-1146

Abstract: Abstract 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.

Keywords: Integer programming; Shortest lattice vector problem; Matrix minors; FPT-algorithm; Lattice width (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-018-0264-z

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