Journal of Combinatorial Optimization

, Volume 35, Issue 4, pp 1128–1146 | Cite as

FPT-algorithms for some problems related to integer programming

  • D. V. Gribanov
  • D. S. Malyshev
  • P. M. Pardalos
  • S. I. Veselov
Article
  • 30 Downloads

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 

Notes

Acknowledgements

Results of Sect. 3 were obtained under financial support of Russian Science Foundation Grant No. 14-41-00039. Results of Sect. 4 were obtained under financial support of Russian Science Foundation Grant No. 17-11-01336. Results of Sect. 5 were obtained under financial support of Russian Foundation for Basic Research, Grant No. 16-31-60008-mol-a-dk, and LATNA laboratory, NRU HSE.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • D. V. Gribanov
    • 1
    • 2
  • D. S. Malyshev
    • 2
  • P. M. Pardalos
    • 2
    • 3
  • S. I. Veselov
    • 1
  1. 1.Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussian Federation
  2. 2.National Research University Higher School of EconomicsNizhny NovgorodRussian Federation
  3. 3.University of FloridaGainesvilleUSA

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