LLL-reduction for Integer Knapsacks

Details LLL-reduction for Integer Knapsacks LLL-reduction for Integer Knapsacks

2010-12-14

arxiv.org/abs/1012.3182v2

Mathematics

Optimization and Control

improved version

Scientific paper

Given an integer mxn matrix A satisfying certain regularity assumptions, a
well-known integer programming problem asks to find an integer point in the
associated knapsack polytope P(A, b)={x: A x= b, x>=0} or determine that no
such point exists. We obtain a LLL-based polynomial time algorithm that solves
the problem subject to a constraint on the location of the vector b.

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