LLL-reduction for integer knapsacks

Iskander Aliev () and Martin Henk ()
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Iskander Aliev: Cardiff University
Martin Henk: Otto-von-Guericke Universität Magdeburg

Journal of Combinatorial Optimization, 2012, vol. 24, issue 4, No 14, 613-626

Abstract: 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.

Keywords: Knapsack problem; Frobenius numbers; Successive minima; Inhomogeneous minimum; Distribution of lattices (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-011-9411-5

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