Distances to Lattice Points in Knapsack Polyhedra
Combinatorics
2018-05-15 v1
Abstract
We give an optimal upper bound for the maximum-norm distance from a vertex of a knapsack polyhedron to its nearest feasible lattice point. In a randomised setting, we show that the upper bound can be significantly improved on average. As a corollary, we obtain an optimal upper bound for the additive integrality gap of integer knapsack problems and show that the integrality gap of a "typical" knapsack problem is drastically smaller than the integrality gap that occurs in a worst case scenario. We also prove that, in a generic case, the integer programming gap admits a natural optimal lower bound.
Cite
@article{arxiv.1805.04592,
title = {Distances to Lattice Points in Knapsack Polyhedra},
author = {Iskander Aliev and Martin Henk and Timm Oertel},
journal= {arXiv preprint arXiv:1805.04592},
year = {2018}
}