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Mexican Conference on Pattern Recognition

MCPR 2018: Pattern Recognition pp 72–81Cite as

A Linear Time Algorithm for Computing #2SAT for Outerplanar 2-CNF Formulas

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10880))

Abstract

Although the satisfiability problem for two Conjunctive Normal Form formulas (2SAT) is polynomial time solvable, it is well known that #2SAT, the counting version of 2SAT is #P-Complete. However, it has been shown that for certain classes of formulas, #2SAT can be computed in polynomial time. In this paper we show another class of formulas for which #2SAT can also be computed in lineal time, the so called outerplanar formulas, e.g. formulas whose signed primal graph is outerplanar. Our algorithm’s time complexity is given by \(O(n+m)\) where n is the number of variables and m the number of clauses of the formula.

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Author information

Authors and Affiliations

  1. Facultad de Ingeniería, UAEM, Toluca, Mexico

    Marco A. López & J. Raymundo Marcial-Romero

  2. Facultad de Ciencias de la Computación, BUAP, Puebla, Mexico

    Guillermo De Ita & Yolanda Moyao

Authors
  1. Marco A. López
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  2. J. Raymundo Marcial-Romero
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  3. Guillermo De Ita
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  4. Yolanda Moyao
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Corresponding author

Correspondence to J. Raymundo Marcial-Romero .

Editor information

Editors and Affiliations

  1. National Institute of Astrophysics, Optics and Electronics, Sta. Maria Tonantzintla, Puebla, Mexico

    José Francisco Martínez-Trinidad

  2. National Institute of Astrophysics, Optics and Electronics, Sta. Maria Tonantzintla, Puebla, Mexico

    Jesús Ariel Carrasco-Ochoa

  3. Autonomous University of Puebla, Puebla, Puebla, Mexico

    José Arturo Olvera-López

  4. University of South Florida, Tampa, Florida, USA

    Sudeep Sarkar

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López, M.A., Marcial-Romero, J.R., De Ita, G., Moyao, Y. (2018). A Linear Time Algorithm for Computing #2SAT for Outerplanar 2-CNF Formulas. In: Martínez-Trinidad, J., Carrasco-Ochoa, J., Olvera-López, J., Sarkar, S. (eds) Pattern Recognition. MCPR 2018. Lecture Notes in Computer Science(), vol 10880. Springer, Cham. https://doi.org/10.1007/978-3-319-92198-3_8

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  • DOI: https://doi.org/10.1007/978-3-319-92198-3_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92197-6

  • Online ISBN: 978-3-319-92198-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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