Before revision:  Inspired by this, we investigate the predictions made by the cavity method for the algorithmic problemsof detecting and recovering a planted signal in a general model of sparse random graphs. The model we study generalizes the well-understood case of the stochastic block model, the less well understood case of random constraint satisfaction problems with planted assignments, as well as "semi-supervised" variants of these models.
After revision:  Inspired by this, we investigate the predictions made by the cavity method for the algorithmic problemsof detecting and recovering a planted signal in a general model of statistical inference problems that includes both community detection in stochastic block models, and all planted constraint satisfaction problems with planted assignments, as well as "semi-supervised" variants of these models.