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Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2019.63
URN: urn:nbn:de:0030-drops-111840
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11184/
Jünger, Michael ;
Mallach, Sven
Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization
Abstract
Solving the NP-hard Maximum Cut or Binary Quadratic Optimization Problem to optimality is important in many applications including Physics, Chemistry, Neuroscience, and Circuit Layout. The leading approaches based on linear/semidefinite programming require the separation of so-called odd-cycle inequalities for solving relaxations within their associated branch-and-cut frameworks. In their groundbreaking work, F. Barahona and A.R. Mahjoub have given an informal description of a polynomial-time separation procedure for the odd-cycle inequalities. Since then, the odd-cycle separation problem has broadly been considered solved. However, as we reveal, a straightforward implementation is likely to generate inequalities that are not facet-defining and have further undesired properties. Here, we present a more detailed analysis, along with enhancements to overcome the associated issues efficiently. In a corresponding experimental study, it turns out that these are worthwhile, and may speed up the solution process significantly.
BibTeX - Entry
@InProceedings{jnger_et_al:LIPIcs:2019:11184,
author = {Michael J{\"u}nger and Sven Mallach},
title = {{Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization}},
booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)},
pages = {63:1--63:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-124-5},
ISSN = {1868-8969},
year = {2019},
volume = {144},
editor = {Michael A. Bender and Ola Svensson and Grzegorz Herman},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11184},
URN = {urn:nbn:de:0030-drops-111840},
doi = {10.4230/LIPIcs.ESA.2019.63},
annote = {Keywords: Maximum cut, Binary quadratic optimization, Integer linear programming}
}
Keywords: |
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Maximum cut, Binary quadratic optimization, Integer linear programming |
Collection: |
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27th Annual European Symposium on Algorithms (ESA 2019) |
Issue Date: |
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2019 |
Date of publication: |
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06.09.2019 |