Experimental results show that certain message passing algorithms, namely, survey propagation, are very effective in finding satisfying assignments in random satisfiable 3CNF formulas. In this paper we make a modest step towards providing rigorous analysis that proves the effectiveness of message passing algorithms for random 3SAT. We analyze the performance of Warning Propagation, a popular message passing algorithm that is simpler than survey propagation. We show that for 3CNF formulas generated under the planted assignment distribution, running warning propagation in the standard way works when the clause-to-variable ratio is a sufficiently large constant. We are not aware of previous rigorous analysis of message passing algorithms for satisfiability instances, though such analysis was performed for decoding of Low Density Parity Check (LDPC) Codes. We discuss some of the differences between results for the LDPC setting and our results.


Random Graph Factor Graph Satisfying Assignment Large Constant Partial Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alekhnovich, M., Ben-Sasson, E.: Linear upper bounds for random walk on small density random 3-cnf. In: Proc. 44th IEEE Symp. on Found. of Comp. Science, pp. 352–361 (2003)Google Scholar
  2. 2.
    Alon, N., Kahale, N.: A spectral technique for coloring random 3-colorable graphs. SIAM J. on Comput. 26(6), 1733–1748 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Braunstein, A., Mezard, M., Zecchina, R.: Survey propagation: an algorithm for satisfiability. Random Structures and Algorithms 27, 201–226 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Broder, A.Z., Frieze, A.M., Upfal, E.: On the satisfiability and maximum satisfiability of random 3-cnf formulas. In: Proc. 4th ACM-SIAM Symp. on Discrete Algorithms, pp. 322–330 (1993)Google Scholar
  5. 5.
    Dubois, O., Boufkhad, Y., Mandler, J.: Typical random 3-sat formulae and the satisfiability threshold. In: Proc. 11th ACM-SIAM Symp. on Discrete Algorithms, pp. 126–127 (2000)Google Scholar
  6. 6.
    Feige, U., Krauthgamer, R.: Finding and certifying a large hidden clique in a semirandom graph. Random Structures and Algorithms 16(2), 195–208 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Feige, U., Vilenchik, D.: A local search algorithm for 3SAT. Technical report, The Weizmann Institute of Science (2004)Google Scholar
  8. 8.
    Flaxman, A.: A spectral technique for random satisfiable 3CNF formulas. In: Proc. 14th ACM-SIAM Symp. on Discrete Algorithms, pp. 357–363 (2003)Google Scholar
  9. 9.
    Friedgut, E.: Sharp thresholds of graph properties, and the k-sat problem. J. Amer. Math. Soc. 12(4), 1017–1054 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Frieze, A.M., McDiarmid, C.: Algorithmic theory of random graphs. Random Structures and Algorithms 10(1-2), 5–42 (1997)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Gallager, T.G.: Low-density parity-check codes. IRE. Trans. Info. Theory IT-8, 21–28 (1962)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Håstad, J.: Some optimal inapproximability results. J. ACM 48(4), 798–859 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hui, C., Frieze, A.M.: Coloring bipartite hypergraphs. In: Proceedings of the 5th International Conference on Integer Programming and Combinatorial Optimization, pp. 345–358 (1996)Google Scholar
  14. 14.
    Kaporis, A.C., Kirousis, L.M., Lalas, E.G.: The probabilistic analysis of a greedy satisfiability algorithm. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 574–585. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Koutsoupias, E., Papadimitriou, C.H.: On the greedy algorithm for satisfiability. Info. Process. Letters 43(1), 53–55 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 47(2), 498–519 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Luby, M., Mitzenmacher, M., Shokrollahi, M.A., Spielman, D.: Analysis of low density parity check codes and improved designs using irregular graphs. In: Proceedings of the 30th ACM Symposium on Theory of Computing, pp. 249–258 (1998)Google Scholar
  18. 18.
    Luby, M., Mitzenmacher, M., Shokrollahi, M.A., Spielman, D.: Efficient erasure correcting codes. IEEE Trans. Info. Theory 47, 569–584 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)Google Scholar
  20. 20.
    Richardson, T., Shokrollahi, A., Urbanke, R.: Design of capacity-approaching irregular low-density parity check codes. IEEE Trans. Info. Theory 47, 619–637 (2001)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Uriel Feige
    • 1
  • Elchanan Mossel
    • 2
  • Dan Vilenchik
    • 3
  1. 1.Micorosoft Research and The Weizmann Institute 
  2. 2.U.C. Berkeley 
  3. 3.Tel Aviv University 

Personalised recommendations