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Classes of cnf-formulas with backtracking trees of exponential or linear average order for exact-satisfiability

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Mathematical Foundations of Computer Science 1988 (MFCS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 324))

Abstract

We analyse the average case behaviour of a simple backtracking algorithm for determining all exact-satisfying truth assignments of CNF-formulas over n variables with r clauses of length s. A truth assignment exact-satisfies a formula, if in every clause exactly one literal is set to true.

  1. 1.

    For the class of formulas given by the parameters n,r, and s a formula computable in polynomial time is derived, by which the average number of nodes in backtracking trees can be determined under the uniform instance distribution.

  2. 2.

    In case where all clauses have length s=3, it is shown that the average number of nodes in backtracking trees is growing exponentially in n, if r=0(n), and it is at most n, if r ≥ 37/40 n 2.

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References

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Authors and Affiliations

  1. Abteilung Informatik, Universität Dortmund, Postfach 500 500, D-4600, Dortmund 50

    Ewald Speckenmeyer

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  1. Ewald Speckenmeyer
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Michal P. Chytil Václav Koubek Ladislav Janiga

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© 1988 Springer-Verlag Berlin Heidelberg

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Speckenmeyer, E. (1988). Classes of cnf-formulas with backtracking trees of exponential or linear average order for exact-satisfiability. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017176

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  • DOI: https://doi.org/10.1007/BFb0017176

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50110-7

  • Online ISBN: 978-3-540-45926-2

  • eBook Packages: Springer Book Archive

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