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A Spectral Method for MAX2SAT in the Planted Solution Model

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Algorithms and Computation (ISAAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4835))

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Abstract

We propose an algorithm using a spectral method, and analyze its average-case performance for MAX2SAT in the planted solution model. In [16], they proposed a distribution \(\mathcal{G}_{n,p,r}\) for MAX2SAT in the planted solution model, as well as a message-passing algorithm. They showed that it solves, \(\textbf{whp}\), MAX2SAT on \(\mathcal{G}_{n,p,r}\) for rather dense formulas, i.e., the expected number of clauses is \(\Omega(n^{1.5}\sqrt{\log n})\). In this paper, we propose an algorithm using a spectral method and a variant of message-passing algorithms, and show that it solves, \(\textbf{whp}\), MAX2SAT on \(\mathcal{G}_{n,p,r}\) for sparser formulas, i.e., the expected number of clauses is Ω(nlogn).

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Masaki Yamamoto

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  1. Masaki Yamamoto
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Takeshi Tokuyama

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© 2007 Springer-Verlag Berlin Heidelberg

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Yamamoto, M. (2007). A Spectral Method for MAX2SAT in the Planted Solution Model. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_12

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  • DOI: https://doi.org/10.1007/978-3-540-77120-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77118-0

  • Online ISBN: 978-3-540-77120-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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