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arXiv · 1805.04592

Distances to Lattice Points in Knapsack Polyhedra

Iskander Aliev·Martin Henk·Timm Oertel
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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.

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Iskander Aliev, Martin Henk, Timm Oertel. 2018-05-11. Distances to Lattice Points in Knapsack Polyhedra. https://arxiv.org/abs/1805.04592

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