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    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

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Projection results for the k-partition problem

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

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Projection results for the k-partition problem. / Fairbrother, Jamie; Letchford, Adam N.
In: Discrete Optimization, Vol. 26, 08.11.2017, p. 97-111.

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

Harvard

Fairbrother, J & Letchford, AN 2017, 'Projection results for the k-partition problem', Discrete Optimization, vol. 26, pp. 97-111. https://doi.org/10.1016/j.disopt.2017.08.001

APA

Fairbrother, J., & Letchford, A. N. (2017). Projection results for the k-partition problem. Discrete Optimization, 26, 97-111. https://doi.org/10.1016/j.disopt.2017.08.001

Vancouver

Fairbrother J, Letchford AN. Projection results for the k-partition problem. Discrete Optimization. 2017 Nov 8;26:97-111. Epub 2017 Sept 6. doi: 10.1016/j.disopt.2017.08.001

Author

Fairbrother, Jamie ; Letchford, Adam N. / Projection results for the k-partition problem. In: Discrete Optimization. 2017 ; Vol. 26. pp. 97-111.

Bibtex

@article{71896102ac3346ef8eb5af344d2d89ba,
title = "Projection results for the k-partition problem",
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 {\textquoteleft}edge-only{\textquoteright} formulation, and project them into a suitable subspace, we obtain the polytopes associated with the {\textquoteleft}node-and-edge{\textquoteright} 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.",
keywords = "Graph partitioning, Polyhedral combinatorics, Branch-and-cut, Semidefinite programming",
author = "Jamie Fairbrother and Letchford, {Adam N.}",
note = "This is the author{\textquoteright}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",
year = "2017",
month = nov,
day = "8",
doi = "10.1016/j.disopt.2017.08.001",
language = "English",
volume = "26",
pages = "97--111",
journal = "Discrete Optimization",
issn = "1572-5286",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Projection results for the k-partition problem

AU - Fairbrother, Jamie

AU - Letchford, Adam N.

N1 - 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

PY - 2017/11/8

Y1 - 2017/11/8

N2 - 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.

AB - 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.

KW - Graph partitioning

KW - Polyhedral combinatorics

KW - Branch-and-cut

KW - Semidefinite programming

U2 - 10.1016/j.disopt.2017.08.001

DO - 10.1016/j.disopt.2017.08.001

M3 - Journal article

VL - 26

SP - 97

EP - 111

JO - Discrete Optimization

JF - Discrete Optimization

SN - 1572-5286

ER -