On the hardness of approximating multicut and sparsest-cut

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). © Birkhäuser Verlag, Basel 2006.