Distances to lattice points in knapsack polyhedra

Aliev I, Henk M, Oertel T (2020)

Publication Type: Journal article

Publication year: 2020


Book Volume: 182

Pages Range: 175-198

Journal Issue: 1-2

DOI: 10.1007/s10107-019-01392-1


We give an optimal upper bound for the ℓ∞-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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Aliev, I., Henk, M., & Oertel, T. (2020). Distances to lattice points in knapsack polyhedra. Mathematical Programming, 182(1-2), 175-198. https://dx.doi.org/10.1007/s10107-019-01392-1


Aliev, Iskander, Martin Henk, and Timm Oertel. "Distances to lattice points in knapsack polyhedra." Mathematical Programming 182.1-2 (2020): 175-198.

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