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Encyclopedia of Algorithms pp 1–6Cite as

Backtracking Based k-SAT Algorithms

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Years and Authors of Summarized Original Work

2005; Paturi, Pudlák, Saks, Zane

Problem Definition

Determination of the complexity of k-CNF satisfiability is a celebrated open problem: given a Boolean formula in conjunctive normal form with at most k literals per clause, find an assignment to the variables that satisfies each of the clauses or declare none exists. It is well known that the decision problem of k-CNF satisfiability is NP-complete for k ≥ 3. This entry is concerned with algorithms that significantly improve the worst-case running time of the naive exhaustive search algorithm, which is poly(n)2n for a formula on n variables. Monien and Speckenmeyer [8] gave the first real improvement by giving a simple algorithm whose running time is \(O(2_{k}^{(1-\upvarepsilon )n})\), with \(\upvarepsilon _{k}> 0\) for all k. In a sequence of results [1, 3, 5–7, 9–12], algorithms with increasingly better running times (larger values of \(\upvarepsilon _{k}\)) have been proposed and...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of California at San Diego, San Diego, CA, USA

    Ramamohan Paturi

  2. Mathematical Institute, Academy of Science of the Czech Republic, Prague, Czech Republic

    Pavel Pudlák

  3. Department of Mathematics, Rutgers, State University of New Jersey, Piscataway,NJ, USA

    Michael Saks

  4. Lucent Technologies, Bell Laboraties, Murray Hill,NJ, USA

    Francis Zane

Authors
  1. Ramamohan Paturi
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  2. Pavel Pudlák
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  3. Michael Saks
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  4. Francis Zane
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Corresponding author

Correspondence to Ramamohan Paturi .

Editor information

Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Paturi, R., Pudlák, P., Saks, M., Zane, F. (2015). Backtracking Based k-SAT Algorithms. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_45-2

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_45-2

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  • Publisher Name: Springer, Boston, MA

  • Online ISBN: 978-3-642-27848-8

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