Abstract
Survey Propagation (SP) is a message passing algorithm that can be viewed as a generalization of the so called Belief Propagation (BP) algorithm used in statistical inference and error correcting codes. In this work we discuss the connections between BP and SP.
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References
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Code and benchmarks available, http://www.ictp.trieste.it/~zecchina/SP/
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Over the n-dimensional hypercube, we say that two vertices are connected if they represent solutions at Hamming distances one. We define a cluster as a connected component over the whole hypercube. SP looks at clusters with a finite fraction of backbone variables [17,1]. Exact enumerations on small random formulas indeed confirm the onset of clustering below αc already for rather small values of n (A. Braunstein, V. Napolano, R. Zecchina, in preparation, 2003). Rigorous results about clustering phenomenon taking place in random K-XOR-SAT can be found in: S. Cocco, O. Dubois,J. Mandler, R. Monasson, Rigorous decimation-based construction of ground pure states for spin glass models on random lattices, Phys. Rev. Lett. 90, 047205 (2003): Mezard, M., Ricci-Tersenghi, F., Zecchina, R.: Two solutions to diluted p-spin models and XORSAT problems J. Stat. Phys. 111, 505 (2003); We mention that for random 3-SAT, there exists another clustering transition at α _ 3.87 [5] where clustering appears and yet no variable is constrained. Such a transition is absent for any K >3.
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Braunstein, A., Zecchina, R. (2004). Survey and Belief Propagation on Random K-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_38
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DOI: https://doi.org/10.1007/978-3-540-24605-3_38
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