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International Computing and Combinatorics Conference

COCOON 2011: Computing and Combinatorics pp 168–179Cite as

A Kolmogorov Complexity Proof of the Lovász Local Lemma for Satisfiability

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6842))

Abstract

Recently, Moser and Tardos [MT10] came up with a constructive proof of the Lovász Local Lemma. In this paper, we give another constructive proof of the lemma, based on Kolmogorov complexity. Actually, we even improve the Local Lemma slightly.

Research supported by DFG grant TH 472/4-1.

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References

  1. Alon, N.: A parallel algorithmic version of the Local Lemma. Random Structures and Algorithms 2(4), 367–378 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alon, N., Spencer, J., Erdős, P.: The probabilistic method. Wiley, Chichester (1992)

    Google Scholar 

  3. Beck, J.: An algorithmic approach to the Lovász Local Lemma. Random Structures and Algorithms 2(4), 343–366 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  4. Erdős, P., Lovász, L.: Problems and results on 3-chromatic hypergraphs and some related questions. In: Hajnal, A., Sós, V. (eds.) Infinite and Finite Sets, pp. 609–627. North-Holland, Amsterdam (1975)

    Google Scholar 

  5. Erdős, P., Spencer, J.: Lopsided Lovász Local Lemma and latin transversals. Discrete Applied Mathematics 30, 151–154 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fortnow, L.: A Kolmogorov complexity proof of the Lovász Local Lemma. Computational Complexity Blog (2009), http://blog.computationalcomplexity.org/2009/06/kolmogorov-complexity-proof-of-lov.html

  7. Gebauer, H.: Disproof of the neighborhood conjecture with implications to SAT. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 764–775. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Graham, R., Knuth, D., Patashnik, O.: Concrete Mathematics, 2nd edn. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  9. Gebauer, H., Moser, R., Scheder, D., Welzl, E.: The Lovász Local Lemma and satisfiability. In: Albers, S., Alt, H., Näher, S. (eds.) Efficient Algorithms. LNCS, vol. 5760, pp. 30–54. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Gebauer, H., Szabó, T., Tardos, G.: The Local Lemma is tight for SAT. In: 22nd ACM-SIAM Symp. on Discrete Algorithms, pp. 664–674 (2011)

    Google Scholar 

  11. Li, M., Vitányi, P.: An introduction to Kolmogorov complexity and its applications, 3rd edn. Springer, Heidelberg (2008)

    Book  MATH  Google Scholar 

  12. McDiarmid, C.: Hypergraph coloring and the Lovász Local Lemma. Discrete Mathematics 167/168, 481–486 (1997)

    Article  MATH  Google Scholar 

  13. Moser, R.A.: Derandomizing the Lovász Local Lemma more efficiently. Technical report (2008), http://arxiv.org/abs/0807.2120

  14. Moser, R.A.: A constructive proof of the Lovász Local Lemma. In: 41th Symposium on Theory on Computing (STOC), pp. 343–350 (2009)

    Google Scholar 

  15. Moser, R., Tardos, G.: A constructive proof of the general Lovász Local Lemma. Journal of the ACM 57(2), 11:1–11:15 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Schöning, U.: Algorithmik. Spektrum Akademischer Verlag, Heidelberg (2001)

    MATH  Google Scholar 

  17. Spencer, J.: Robin Moser makes Lovász Local Lemma algorithmic! (2010), http://cs.nyu.edu/spencer/moserlovasz1.pdf

  18. Srinivasan, A.: Improved algorithmic versions of the Lovász Local Lemma. In: 9th ACM-SIAM Symp. on Discrete Algorithms, pp. 611–620 (2008)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Aalen University, 73430, Aalen, Germany

    Jochen Messner & Thomas Thierauf

Authors
  1. Jochen Messner
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  2. Thomas Thierauf
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, 78539, Edinburg, TX, USA

    Bin Fu

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

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Messner, J., Thierauf, T. (2011). A Kolmogorov Complexity Proof of the Lovász Local Lemma for Satisfiability. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-22685-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22684-7

  • Online ISBN: 978-3-642-22685-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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