Projection results for the k-partition problem
Fairbrother, Jamie and Letchford, Adam N.
(2017)
Projection results for the k-partition problem.
Discrete Optimization, 26.
pp. 97-111.
ISSN 1572-5286
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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.
Item Type:
Journal Article
Journal or Publication Title:
Discrete Optimization
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1700/1703
Subjects:
?? graph partitioningpolyhedral combinatoricsbranch-and-cutsemidefinite programmingcomputational theory and mathematicstheoretical computer scienceapplied mathematicsdiscipline-based research ??
Deposited On:
12 Sep 2017 14:34
Last Modified:
02 Jul 2025 01:18