A Message Passing Algorithm for MAX2SAT

We propose a simple and deterministic algorithm for solving MAX2SAT, which runs O(n(n+m)) time where n and m are respectively the number of variables and clauses. For discussing its average case performance, we propose one natural “planted solution model”; a way to generate a MAX2SAT instance under a certain distribution defined by parameters p and r. We first show that if p = Ω(ln n/n) and p ≥ 9r, then with high probability the planted solutions (there are four planted solutions) are only the optimal solution, unsatisfying 3rn2 clauses out of (on average) 2pn2 + 8rn2 clauses. Then under this planted solution model we show that, for some constant 2 > 0, our algorithm yields one of the planted solutions with high probability if p− r ≥ n−1/2+2.