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We introduce a version of the cavity method for diluted mean-field spinmodels that allows the computation of thermodynamic quantities similar to theFranz-Parisi quenched potential in sparse random graph models. This method isdeveloped in the particular case of partially decimated random constraintsatisfaction problems. This allows to develop a theoretical understanding of aclass of algorithms for solving constraint satisfaction problems, in whichelementary degrees of freedom are sequentially assigned according to theresults of a message passing procedure (belief-propagation). We confront thistheoretical analysis to the results of extensive numerical simulations.

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