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    Rights statement: This is the author’s version of a work that was accepted for publication in Operations Research Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Operations Research Letters, 49, 4, 2021 DOI: 10.1016/j.orl.2021.05.011

    Accepted author manuscript, 296 KB, PDF document

    Embargo ends: 30/11/22

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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On the complexity of surrogate and group relaxation for integer linear programs

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>31/07/2021
<mark>Journal</mark>Operations Research Letters
Issue number4
Volume49
Number of pages5
Pages (from-to)530-534
Publication StatusPublished
Early online date31/05/21
<mark>Original language</mark>English

Abstract

Surrogate and group relaxation have been used to compute bounds for various integer linear programming problems. We prove that (a) when only inequalities are surrogated, the surrogate dual is NP-hard, but solvable in pseudo-polynomial time under certain conditions; (b) when equations are surrogated, the surrogate dual exhibits unusual complexity behaviour; (c) the group relaxation is NP-hard for the
integer and 0-1 knapsack problems, and strongly NP-hard for the set packing problem.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Operations Research Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Operations Research Letters, vol. 49, issue 4, 2021 DOI:10.1016/j.orl.2021.05.011