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

Federico Ricci-Tersenghi, Guilhem Semerjian
2009 Journal of Statistical Mechanics: Theory and Experiment  
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
more » ... ly assigned according to the results of a message passing procedure (belief-propagation). We confront this theoretical analysis to the results of extensive numerical simulations.
doi:10.1088/1742-5468/2009/09/p09001 fatcat:76d27nbyqrfnbmt66o77ola4wq