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In this paper, we propose a novel approximation algorithm (RelaxSAT) for MIN-ONE SAT. RelaxSAT generates a set of constraints from the objective function to guide the search. The constraints are gradually relaxed to eliminate the conflicts with the original Boolean SAT formula until a solution is found. The experiments demonstrate that RelaxSAT is able to handle very large instances which cannot be solved by existing MIN-ONE algorithms; furthermore, very tight bounds on the solution were obtained with one to two orders of magnitude speedup.