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[[Johan Håstad]] has shown that, assuming P ≠ NP, no polynomial-time algorithm for MAX 3SAT can achieve a performance ratio exceeding 7/8, even when restricted to satisfiable instances of the problem. Their algorithm is therefore optimal in this sense.<ref>J. Hastad. "Some optimal inapproximability results." In proceedings of the 29th ''ACM STOC'', 1-10, 1997</ref>
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