LIPIcs.STACS.2013.526.pdf
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On the practically interesting instances of MAXCUT
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30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication date: 2013-02-26
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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)
https://doi.org/10.4230/LIPIcs.STACS.2013.526
https://doi.org/10.4230/LIPIcs.STACS.2013.526
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.
Keywords
- MAXCUT
- Clustering
- Hardness in practice
- Stability
- Non worst-case analysis
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