Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Parameterized SAT

2003; Szeider
  • Stefan Szeider
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_283

Keywords and Synonyms

Structural parameters for SAT              

Problem Definition

Much research has been devoted to finding classes of propositional formulas in conjunctive normal form (CNF) for which the recognition problem as well as the propositional satisfiability problem (SAT) can be decided in polynomial time. Some of these classes form infinite chains \( { C_1 \subset C_2 \subset \cdots } \)

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Cook, S.A.: The complexity of theorem‐proving procedures. In: Proc. 3rd Annual Symp. on Theory of Computing, Shaker Heights, OH 1971, pp. 151–158Google Scholar
  2. 2.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Monographs in Computer Science. Springer, Berlin (1999)Google Scholar
  3. 3.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Texts in Theoretical Computer Science, vol. XIV. An EATCS Series. Springer, Berlin (2006)Google Scholar
  4. 4.
    Gottlob, G., Scarcello, F., Sideri, M.: Fixed‐parameter complexity in AI and nonmonotonic reasoning. Artif. Intell. 138, 55–86 (2002)MathSciNetGoogle Scholar
  5. 5.
    Gottlob, G., Szeider, S.: Fixed‐parameter algorithms for artificial intelligence, constraint satisfaction, and database problems. Comput. J., Special Issue on Parameterized Complexity, Advanced Access (2007) Google Scholar
  6. 6.
    Niedermeier, R.: Invitation to Fixed‐Parameter Algorithms, Oxford Lecture Series in Mathematics and Its Applications. Oxford University Press, Oxford, UK (2006)Google Scholar
  7. 7.
    Nishimura, N., Ragde, P., Szeider, S.: Detecting backdoor sets with respect to Horn and binary clauses. In: Informal proceedings of SAT 2004, 7th International Conference on Theory and Applications of Satisfiability Testing, Vancouver, BC, Canada, 10–13 May 2004, pp. 96–103Google Scholar
  8. 8.
    Nishimura, N., Ragde, P., Szeider, S.: Solving SAT using vertex covers. Acta Inf. 44(7–8), 509–523 (2007)MathSciNetGoogle Scholar
  9. 9.
    Papadimitriou, C.H., Wolfe, D.: The complexity of facets resolved. J. Comput. Syst. Sci. 37, 2–13 (1988)MathSciNetGoogle Scholar
  10. 10.
    Samer, M., Szeider, S.: Algorithms for propositional model counting. In: Proceedings of LPAR 2007, 14th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Yerevan, Armenia, 15–19 October 2007. Lecture Notes in Computer Science, vol. 4790, pp. 484–498. Springer, Berlin (2007)Google Scholar
  11. 11.
    Szeider, S.: Minimal unsatisfiable formulas with bounded clause‐variable difference are fixed‐parameter tractable. J. Comput. Syst. Sci. 69, 656–674 (2004)MathSciNetGoogle Scholar
  12. 12.
    Szeider, S.: On fixed‐parameter tractable parameterizations of SAT. In: Giunchiglia, E., Tacchella, A. (eds.) Theory and Applications of Satisfiability, 6th International Conference, SAT 2003, Selected and Revised Papers. Lecture Notes in Computer Science, vol. 2919, pp. 188–202. Springer, Berlin (2004)Google Scholar
  13. 13.
    Williams, R., Gomes, C., Selman, B.: On the connections between backdoors, restarts, and heavy‐tailedness in combinatorial search, In: informal proceedings of SAT 2003 (Sixth International Conference on Theory and Applications of Satisfiability Testing, 5–8 May 2003, S. Margherita Ligure – Portofino, Italy), 2003, pp. 222–230Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Stefan Szeider
    • 1
  1. 1.Department of Computer ScienceDurham UniversityDurhamUK