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We show that the Multicut, Sparsest-Cut, and Min-2CNF ≡ Deletion problems are NP-hard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot (2002). A quantitatively stronger version of the conjecture implies an inapproximability factor of Ω(√log log n).
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Chawla et al. (2006) studied this question.
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