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DOI: 10.4230/LIPIcs.STACS.2013.526

On the practically interesting instances of MAXCUT

Authors: Yonatan Bilu, Amit Daniely, Nati Linial, and Michael Saks

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract

For many optimization problems, the instances of practical interest often occupy just a tiny part of the algorithm's space of instances. Following (Y. Bilu and N. Linial, 2010), we apply this perspective to MAXCUT, viewed as a clustering problem. Using a variety of techniques, we investigate practically interesting instances of this problem. Specifically, we show how to solve in polynomial time distinguished, metric, expanding and dense instances of MAXCUT under mild stability assumptions. In particular, (1 + epsilon)-stability (which is optimal) suffices for metric and dense MAXCUT. We also show how to solve in polynomial time Omega(sqrt(n))-stable instances of MAXCUT, substantially improving the best previously known result.

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Yonatan Bilu, Amit Daniely, Nati Linial, and Michael Saks. On the practically interesting instances of MAXCUT. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 526-537, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{bilu_et_al:LIPIcs.STACS.2013.526,
  author =	{Bilu, Yonatan and Daniely, Amit and Linial, Nati and Saks, Michael},
  title =	{{On the practically interesting instances of MAXCUT}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{526--537},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.526},
  URN =		{urn:nbn:de:0030-drops-39625},
  doi =		{10.4230/LIPIcs.STACS.2013.526},
  annote =	{Keywords: MAXCUT, Clustering, Hardness in practice, Stability, Non worst-case analysis}
}

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On the practically interesting instances of MAXCUT

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