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On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms


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      We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in the particular case of partially decimated random constraint satisfaction problems. This allows to develop a theoretical understanding of a class of algorithms for solving constraint satisfaction problems, in which elementary degrees of freedom are sequentially assigned according to the results of a message passing procedure (belief-propagation). We confront this theoretical analysis to the results of extensive numerical simulations.

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      J Stat. Mech. P09001 (2009)
      32 pages, 24 figures
      cond-mat.dis-nn cond-mat.stat-mech cs.DM


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