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 [STOC, 2002]. A quantitatively stronger version of the conjecture implies ...

An errorless circuit for a Boolean function is one that outputs the correct answer or "don't know" on each input (and never outputs the wrong answer). The goal of errorless hardness amplification is to show that if f has no size s errorless circuit that ...

The Multicut problem, given a graph G, a set of terminal pairs $\mathcal{T}=\{(s_i,t_i)\ |\ 1\leq i\leq r\}$, and an integer $p$, asks whether one can find a cutset consisting of at most $p$ nonterminal vertices that separates all the terminal pairs, i.e., ...