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  • kpp-projection

    Rights statement: This is the author’s version of a work that was accepted for publication in Discrete Optimization. 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 Discrete Optimization, 26, 2017 DOI: 10.1016/j.disopt.2017.08.001

    Accepted author manuscript, 335 KB, PDF document

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

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Projection results for the k-partition problem

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
<mark>Journal publication date</mark>8/11/2017
<mark>Journal</mark>Discrete Optimization
Volume26
Number of pages15
Pages (from-to)97-111
Publication StatusPublished
Early online date6/09/17
<mark>Original language</mark>English

Abstract

The k-partition problem is an NP-hard combinatorial optimisation problem with many applications. Chopra and Rao introduced two integer programming formulations of this problem, one having both node and edge variables, and the other having only edge variables. We show that, if we take the polytopes associated with the ‘edge-only’ formulation, and project them into a suitable subspace, we obtain the polytopes associated with the ‘node-and-edge’ formulation. This result enables us to derive new valid inequalities and separation algorithms, and also to shed new light on certain SDP relaxations. Computational results are also presented.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Discrete Optimization. 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 Discrete Optimization, 26, 2017 DOI: 10.1016/j.disopt.2017.08.001