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Approximating Almost All Instances of Max-Cut Within a Ratio Above the Håstad Threshold

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

We give a deterministic polynomial-time algorithm which for any given average degree d and asymptotically almost all random graphs G in \(\mathcal G(n, m= \lfloor\frac{d}{2}n\rfloor)\) outputs a cut of G whose ratio (in cardinality) with the maximum cut is at least 0.952. We remind the reader that it is known that unless P=NP, for no constant ε>0 is there a Max-Cut approximation algorithm that for all inputs achieves an approximation ratio of (16/17) +ε (16/17 < 0.94118).

The authors are partially supported by European Social Fund (ESF), Operational Program for Educational and Vocational Training II (EPEAEK II), and particularly Pythagoras. The second author is partially supported by Future and Emerging Technologies programme of the EU under contract 001907 “Dynamically Evolving, Large-Scale Information Systems (DELIS).”

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Author information

Authors and Affiliations

  1. Department of Computer Engineering and Informatics, University of Patras, GR-265 04, Patras, Greece

    A. C. Kaporis, L. M. Kirousis & E. C. Stavropoulos

  2. Research Academic Computer Technology Institute, P.O. Box 1122, GR-261 10, Patras, Greece

    L. M. Kirousis

Authors
  1. A. C. Kaporis
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  2. L. M. Kirousis
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  3. E. C. Stavropoulos
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Kaporis, A.C., Kirousis, L.M., Stavropoulos, E.C. (2006). Approximating Almost All Instances of Max-Cut Within a Ratio Above the Håstad Threshold. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_40

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  • DOI: https://doi.org/10.1007/11841036_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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