Modified Belief Propagation: an Algorithm for Optimization Problems

Belief propagation is a well known algorithm to solve various optimization problems, such as error correcting codes graph colouring and satisfiability problems. It generally works well in areas where the replica symmetric approximation holds, but breaks down when replica symmetry breaking occurs. Alternatives such as Survey Propagation have been proposed with great success, but are generally limited to the zero temperature limit. We propose a simple modification to Belief Propagation that can also successfully deal with finite temperature scenarios, and illustrate its efficiency on several examples.