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Local Search and SAT

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Exact Exponential Algorithms

Part of the book series: Texts in Theoretical Computer Science. An EATCS Series ((TTCS))

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Abstract

In Chap. 2, we discuss a branching algorithm for the k-Satisfiability problem. In this chapter we consider more techniques for solving k-SAT. Both techniques are based on performing local search in balls in the Hamming space around some assignments. The first algorithm randomly chooses an assignment and performs a random walk of short length (in Hamming distance) to search for the solution. The second algorithm is deterministic and uses a similar idea; but instead of using a random walk, it finds a covering of the Hamming space by balls of specified radius and performs a search inside these balls.

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References

  1. Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science (FOCS 1999), pp. 410–414. IEEE (1999)

    Google Scholar 

  2. Schöning, U.: A probabilistic algorithm for k-SAT based on limited local search and restart. Algorithmica 32(4), 615–623 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Papadimitriou, C.H.: On selecting a satisfying truth assignment (extended abstract). In: Proceedings of the 32nd annual Symposium on Foundations of Computer Science (FOCS 1991), pp. 163–169. IEEE (1991).

    Google Scholar 

  4. Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, New York, NY, USA (2005)

    MATH  Google Scholar 

  5. Feller, W.: An introduction to probability theory and its applications. Vol. I, third edn. John Wiley & Sons Inc., New York (1968)

    Google Scholar 

  6. Paturi, R., Pudlák, P., Saks, M.E., Zane, F.: An improved exponential-time algorithm for k-SAT. J. ACM 52(3), 337–364 (2005).

    Article  MathSciNet  Google Scholar 

  7. Paturi, R., Pudlák, P., Zane, F.: Satisfiability coding lemma. Chicago J. Theor. Comput. Sci. 1999, Article 11 (1999).

    Google Scholar 

  8. Iwama, K., Tamaki, S.: Improved upper bounds for 3-SAT. In: Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), p. 328. SIAM (2004)

    Google Scholar 

  9. Hofmeister, T., Schöning, U., Schuler, R., Watanabe, O.: Randomized algorithms for 3-SAT. Theory Comput. Syst. 40(3), 249–262 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  10. Rolf, D.: Improved bound for the PPSZ/Schöning-algorithm for 3-SAT. J. Satisfiability, Boolean Modeling and Computation 1(2), 111–122 (2006)

    MATH  Google Scholar 

  11. Schöning, U.: Algorithmics in exponential time. In: Proceedings of the 22nd International Symposium on Theoretical Aspects of Computer Science (STACS 2005), Lecture Notes in Comput. Sci., vol. 3404, pp. 36–43. Springer (2005)

    Google Scholar 

  12. Iwama, K.: Worst-case upper bounds for k-SAT. Bulletin of the EATCS 82, 61–71 (2004)

    MATH  MathSciNet  Google Scholar 

  13. Dantsin, E., Goerdt, A., Hirsch, E.A., Kannan, R., Kleinberg, J., Papadimitriou, C., Raghavan, P., Schöning, U.: A deterministic (2-2/(k+1))n algorithm for k-SAT based on local search. Theor. Comp. Sci. 289(1), 69–83 (2002)

    Article  MATH  Google Scholar 

  14. Hochbaum, D.S. (ed.): Approximation algorithms for NP-hard problems. PWS Publishing Co., Boston, MA, USA (1997)

    Google Scholar 

  15. Brueggemann, T., Kern, W.: An improved deterministic local search algorithm for 3-SAT. Theor. Comp. Sci. 329(1-3), 303–313 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Scheder, D.: Guided search and a faster deterministic algorithm for 3-SAT. In: Proceedings of the 8th Latin American Symposium on Theoretical Informatics (LATIN 2008), Lecture Notes in Comput. Sci., vol. 4957, pp. 60–71. Springer (2008)

    Google Scholar 

  17. Dantsin, E., Hirsch, E.A.:Worst-case upper bounds. In: Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, chap. 12, pp. 403–424. IOS Press (2009)

    Google Scholar 

  18. Feder T., Motwani, R.: Worst-case time bounds for coloring and satisfiability problems. J. Algorithms 45(2), 192-201 (2002).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Bergen, Inst. Informatics, PO Box 7800, 5020, Bergen, Norway

    Prof. Dr. Fedor V. Fomin

  2. Dépt. Informatique Ile du Saulcy, Université Paul Verlaine - Metz, LITA, UFR MIM, 57045, Cedex 1, France

    Prof. Dieter Kratsch

Authors
  1. Prof. Dr. Fedor V. Fomin
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  2. Prof. Dieter Kratsch
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Correspondence to Fedor V. Fomin .

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Fomin, F.V., Kratsch, D. (2010). Local Search and SAT. In: Exact Exponential Algorithms. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16533-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-16533-7_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16532-0

  • Online ISBN: 978-3-642-16533-7

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