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 [STOC, 2002]. A quantitatively stronger version of the conjecture implies an inapproximability factor of Ω( √ log log n).
Shuchi Chawla, Robert Krauthgamer, Ravi Kumar, Yuv