Aliev, Iskander, Henk, Martin and Oertel, Timm
2020.
Distances to lattice points in knapsack polyhedra.
Mathematical Programming
182
10.1007/s10107-019-01392-1
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Official URL: https://doi.org/10.1007/s10107-019-01392-1
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 |
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Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Publisher: | Springer Verlag |
ISSN: | 0025-5610 |
Related URLs: | |
Date of First Compliant Deposit: | 2 April 2019 |
Date of Acceptance: | 11 March 2019 |
Last Modified: | 16 Nov 2020 16:00 |
URI: | http://orca.cf.ac.uk/id/eprint/121278 |
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