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On Fixed-Parameter Tractable Parameterizations of SAT

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Theory and Applications of Satisfiability Testing (SAT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2919))

Abstract

We survey and compare parameterizations of the propositional satisfiability problem (SAT) in the framework of Parameterized Complexity (Downey and Fellows, 1999). In particular, we consider (a) parameters based on structural graph decompositions (tree-width, branch-width, and clique-width), (b) a parameter emerging from matching theory (maximum deficiency), and (c) a parameter defined by translating clause-sets into certain implicational formulas (falsum number).

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References

  1. Aharoni, R., Linial, N.: Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas. J. Combin. Theory Ser. A 43, 196–204 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alekhnovich, M., Razborov, A.A.: Satisfiability, branch-width and Tseitin tautologies. In: 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2002), pp. 593–603 (2002)

    Google Scholar 

  3. Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM J. Algebraic Discrete Methods 8(2), 277–284 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bacchus, F., Dalmao, S., Pitassi, T.: Algorithms and complexity results for #SAT and Bayesian Inference. In: 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003 (2003) (to appear)

    Google Scholar 

  5. Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25(6), 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theoret. Comput. Sci. 209(1-2), 1–45 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cesati, M.: Compendium of parameterized problems (2001), http://bravo.ce.uniroma2.it/home/cesati/research/

  8. Cook, S.A.: An exponential example for analytic tableaux (1972) (manuscript)

    Google Scholar 

  9. Courcelle, B., Makowsky, J.A., Rotics, U.: On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic. Discr. Appl. Math. 108(1-2), 23–52 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Courcelle, B., Olariu, S.: Upper bounds to the clique width of graphs. Discr. Appl. Math. 101(1-3), 77–114 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Davis, M., Logemann, G., Loveland, D.: A machine program for theoremproving. Comm. ACM 5, 394–397 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  12. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  13. Fleischner, H., Földes, S., Szeider, S.: Remarks on the concept of robust algorithm. Technical Report RRR 26-2001, Rutgers Center for Operations Research (RUTCOR) (April 2001)

    Google Scholar 

  14. Fleischner, H., Kullmann, O., Szeider, S.: Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference. Theoret. Comput. Sci. 289(1), 503–516 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Franco, J., Goldsmith, J., Schlipf, J., Speckenmeyer, E., Swaminathan, R.P.: An algorithm for the class of pure implicational formulas. Discr. Appl. Math. 97, 89–106 (1999)

    Article  MathSciNet  Google Scholar 

  16. Golumbic, M.C., Rotics, U.: On the clique-width of some perfect graph classes. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 423–443. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  17. Gottlob, G., Pichler, R.: Hypergraphs in model checking: Acyclicity and hypertree-width versus clique-width. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 708–719. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  18. Gottlob, G., Scarcello, F., Sideri, M.: Fixed-parameter complexity in AI and nonmonotonic reasoning. Artificial Intelligence 138(1-2), 55–86 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Heusch, P.: The complexity of the falsifiability problem for pure implicational formulas. Discr. Appl. Math. 96/97, 127–138 (1999)

    Article  MathSciNet  Google Scholar 

  20. Heusch, P., Porschen, S., Speckenmeyer, E.: Improving a fixed parameter tractability time bound for the shadow problem. Technical Report 2001-425, Universität zu Köln (2001)

    Google Scholar 

  21. Kullmann, O.: Investigating a general hierarchy of polynomially decidable classes of CNF’s based on short tree-like resolution proofs. Technical Report TR99–041, Electronic Colloquium on Computational Complexity, ECCC (1999)

    Google Scholar 

  22. Kullmann, O.: An application of matroid theory to the SAT problem. In: Fifteenth Annual IEEE Conference on Computational Complexity, pp. 116–124 (2000)

    Google Scholar 

  23. Pretolani, D.: Hierarchies of polynomially solvable satisfiability problems. Ann. Math. Artif. Intell. 17(3-4), 339–357 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  24. Robertson, N., Seymour, P.D.: Graph minors, II. Algorithmic aspects of treewidth. J. Algorithms 7(3), 309–322 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  25. Robertson, N., Seymour, P.D.: Graph minors, X. Obstructions to treedecomposition. J. Combin. Theory Ser. B 52(2), 153–190 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  26. Robertson, N., Seymour, P.D.: Graph minors, XIII. The disjoint paths problem. J. Combin. Theory Ser. B 63(1), 65–110 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  27. Spinrad, J.P.: Representations of graphs. Book manuscript, Vanderbilt University (1997)

    Google Scholar 

  28. Szeider, S.: Generalizations of matched CNF formulas. Ann. Math. Artif. Intell., Special issue with selected papers from the 5th Int. Symp. on the Theory and Applications of Satisfiability Testing, SAT 2002 (2002) (to appear)

    Google Scholar 

  29. Szeider, S.: Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 548–558. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  30. Urquhart, A.: The complexity of propositional proofs. Bull. of Symbolic Logic 1(4), 425–467 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  31. Yannakakis, M.: Algorithms for acyclic database schemes. In: Zaniolo, C., Delobel, C. (eds.) Very Large Data Bases, 7th International Conference, Cannes, France, September 9-11, pp. 81–94. IEEE Computer Society, Los Alamitos (1981)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto, M5S 3G4, Toronto, Ontario, Canada

    Stefan Szeider

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  1. Stefan Szeider
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Editor information

Editors and Affiliations

  1. DIST, Università di Genova, Viale Causa, 13, 16145, Genova, Italy

    Enrico Giunchiglia  & Armando Tacchella  & 

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Szeider, S. (2004). On Fixed-Parameter Tractable Parameterizations of SAT. In: Giunchiglia, E., Tacchella, A. (eds) Theory and Applications of Satisfiability Testing. SAT 2003. Lecture Notes in Computer Science, vol 2919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24605-3_15

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  • DOI: https://doi.org/10.1007/978-3-540-24605-3_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20851-8

  • Online ISBN: 978-3-540-24605-3

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