Distances to lattice points in knapsack polyhedra

Aliev, Iskander, Henk, Martin and Oertel, Timm 2019. Distances to lattice points in knapsack polyhedra. Mathematical Programming 10.1007/s10107-019-01392-1

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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.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer Verlag
ISSN:	0025-5610
Date of First Compliant Deposit:	2 April 2019
Date of Acceptance:	11 March 2019
Last Modified:	17 Apr 2019 13:56
URI:	http://orca.cf.ac.uk/id/eprint/121278

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