LLL-reduction for integer knapsacks

Authors:
Iskander Aliev;Martin Henk
Affiliations:
School of Mathematics and Wales Institute of Mathematical and Computational Sciences, Cardiff University, Cardiff, UK;Fakultät für Mathematik, Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany 39106
Venue:
Journal of Combinatorial Optimization
Year:
2012

Citing 6
Cited 0

Theory of linear and integer programming

Theory of linear and integer programming
On Lova´sz' lattice reduction and the nearest lattice point problem

Combinatorica
Hard Equality Constrained Integer Knapsacks

Mathematics of Operations Research
Frobenius Problem and the Covering Radius of a Lattice

Discrete & Computational Geometry
Approximate Nonlinear Optimization over Weighted Independence Systems

SIAM Journal on Discrete Mathematics
Feasibility of Integer Knapsacks

SIAM Journal on Optimization

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Abstract

Given a matrix A驴驴 m脳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.