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LLL-reduction for integer knapsacks

Author

Listed:
  • Iskander Aliev

    (Cardiff University)

  • Martin Henk

    (Otto-von-Guericke Universität Magdeburg)

Abstract

Given a matrix A∈ℤ m×n satisfying certain regularity assumptions, a well-known integer programming problem asks to find an integer point in the associated knapsack polytope or determine that no such point exists. We obtain an LLL-based polynomial time algorithm that solves the problem subject to a constraint on the location of the vector b.

Suggested Citation

  • Iskander Aliev & Martin Henk, 2012. "LLL-reduction for integer knapsacks," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 613-626, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9411-5
    DOI: 10.1007/s10878-011-9411-5
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    References listed on IDEAS

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    1. Friedrich Eisenbrand & Gennady Shmonin, 2008. "Parametric Integer Programming in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 839-850, November.
    2. Hansen, Paul & Ryan, Jennifer, 1996. "Testing integer knapsacks for feasibility," European Journal of Operational Research, Elsevier, vol. 88(3), pages 578-582, February.
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    Cited by:

    1. Karen Aardal & Frederik von Heymann, 2014. "On the Structure of Reduced Kernel Lattice Bases," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 823-840, August.

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