License: 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
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J√ľnger, Michael ; Mallach, Sven

Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization

LIPIcs-ESA-2019-63.pdf (0.8 MB)


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

  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 =		{},
  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: Maximum cut, Binary quadratic optimization, Integer linear programming
Collection: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019

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