Integer Points in Knapsack Polytopes and s-covering Radius
Combinatorics
2012-11-15 v1 Number Theory
Optimization and Control
Abstract
Given an integer matrix A satisfying certain regularity assumptions, we consider for a positive integer s the set F_s(A) of all integer vectors b such that the associated knapsack polytope P(A,b)={x: Ax=b, x non-negative} contains at least s integer points. In this paper we investigate the structure of the set F_s(A) sing the concept of s-covering radius. In particular, in a special case we prove an optimal lower bound for the s-Frobenius number.
Cite
@article{arxiv.1211.3269,
title = {Integer Points in Knapsack Polytopes and s-covering Radius},
author = {Iskander Aliev and Martin Henk and Eva Linke},
journal= {arXiv preprint arXiv:1211.3269},
year = {2012}
}