Abstract
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.
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References
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)
Alon, N., Kahale, N.: A spectral technique for coloring random 3-colorable graphs. SIAM J. on Comput. 26(6), 1733–1748 (1997)
Braunstein, A., Mezard, M., Zecchina, R.: Survey propagation: an algorithm for satisfiability. Random Structures and Algorithms 27, 201–226 (2005)
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)
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)
Feige, U., Krauthgamer, R.: Finding and certifying a large hidden clique in a semirandom graph. Random Structures and Algorithms 16(2), 195–208 (2000)
Feige, U., Vilenchik, D.: A local search algorithm for 3SAT. Technical report, The Weizmann Institute of Science (2004)
Flaxman, A.: A spectral technique for random satisfiable 3CNF formulas. In: Proc. 14th ACM-SIAM Symp. on Discrete Algorithms, pp. 357–363 (2003)
Friedgut, E.: Sharp thresholds of graph properties, and the k-sat problem. J. Amer. Math. Soc. 12(4), 1017–1054 (1999)
Frieze, A.M., McDiarmid, C.: Algorithmic theory of random graphs. Random Structures and Algorithms 10(1-2), 5–42 (1997)
Gallager, T.G.: Low-density parity-check codes. IRE. Trans. Info. Theory IT-8, 21–28 (1962)
Håstad, J.: Some optimal inapproximability results. J. ACM 48(4), 798–859 (2001)
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)
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)
Koutsoupias, E., Papadimitriou, C.H.: On the greedy algorithm for satisfiability. Info. Process. Letters 43(1), 53–55 (1992)
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)
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)
Luby, M., Mitzenmacher, M., Shokrollahi, M.A., Spielman, D.: Efficient erasure correcting codes. IEEE Trans. Info. Theory 47, 569–584 (2001)
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)
Richardson, T., Shokrollahi, A., Urbanke, R.: Design of capacity-approaching irregular low-density parity check codes. IEEE Trans. Info. Theory 47, 619–637 (2001)
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Feige, U., Mossel, E., Vilenchik, D. (2006). Complete Convergence of Message Passing Algorithms for Some Satisfiability Problems. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2006 2006. Lecture Notes in Computer Science, vol 4110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11830924_32
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DOI: https://doi.org/10.1007/11830924_32
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