Belief Propagation is introduced as an algorithm for finding the minima of the Bethe-Peierls free energy, with focus on heterogeneous models on graphs. The main properties of the algorithm are discussed, and applications to problems in several domains (physics, computer science, information theory) are reviewed. Various generalizations and extensions of these concepts and methods are also briefly touched: generalized belief propagation as an algorithm for Kikuchi's cluster variational method, dynamical and quantum problems, survey propagation

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