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A Fast and Simple Parallel Algorithm for the Monotone Duality Problem

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Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5555))

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Abstract

We consider the monotone duality problem i.e., checking whether given monotone CNF ϕ and DNF ψ are equivalent, which is a prominent open problem in NP-completeness. We construct a fast and simple parallel algorithms for the problem, that run in polylogarithmic time by using quasi-polynomially many processors. The algorithm exhibits better parallel time complexity of the existing algorithms of Elbassioni [11]. By using a different threshold of the degree parameter ε of ϕ in the algorithm, we also present a stronger bound on the number of processors for polylogarithmic-time parallel computation and improves over the previously best known bound on the sequential time complexity of the problem in the case when the magnitudes of |ϕ|, |ψ| and n are different, e.g., |ψ| = |ϕ|α ≫ n for α> 1, where n denotes the number of variables. Furthermore, we show that, for several interesting well-known classes of monotone CNFs ϕ such as bounded degree, clause-size, and intersection-size, our parallel algorithm runs polylogarithmic time by using polynomially many processors.

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Authors and Affiliations

  1. RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ, 08854-8003, USA

    Endre Boros

  2. Department of Mathematical Informatics, University of Tokyo, Tokyo, 113-8656, Japan

    Kazuhisa Makino

Authors
  1. Endre Boros
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  2. Kazuhisa Makino
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Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504 Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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© 2009 Springer-Verlag Berlin Heidelberg

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Boros, E., Makino, K. (2009). A Fast and Simple Parallel Algorithm for the Monotone Duality Problem. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-02927-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02926-4

  • Online ISBN: 978-3-642-02927-1

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