English

LLL-reduction for Integer Knapsacks

Optimization and Control 2011-08-01 v2 Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1012.3182,
  title  = {LLL-reduction for Integer Knapsacks},
  author = {Iskander Aliev and Martin Henk},
  journal= {arXiv preprint arXiv:1012.3182},
  year   = {2011}
}

Comments

improved version

R2 v1 2026-06-21T16:58:46.038Z