We propose a "planted solution model" for discussing the average-case complexity of the MAX-2SAT problem. We show that for a large range of parameters, the planted solution (more precisely, one of the planted solution pair) is the optimal solution for the generated instance with high probability. We then give a simple linear time algorithm based on a message passing method, and we prove that it solves the MAX-2SAT problem with high probability under our planted solution model.
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