Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?

In this paper we show a reduction from the Unique Games problem to the problem of approximating MAX-CUT to within a factor of GW + , for all > 0; here GW .878567 denotes the approximation ratio achieved by the Goemans-Williamson algorithm [25]. This implies that if the Unique Games Conjecture of Khot [36] holds then the Goemans-Williamson approximation algorithm is optimal. Our result indicates that the geometric nature of the Goemans-Williamson algorithm might be intrinsic to the MAX-CUT problem. Our reduction relies on a theorem we call Majority Is Stablest. This was introduced as a conjecture in the original version of this paper, and was subsequently confirmed in [42]. A stronger version of this conjecture called Plurality Is Stablest is still open, although [42] contains a proof of an asymptotic version of it. Our techniques extend to several other two-variable constraint satisfaction problems. In particular, subject to the Unique Games Conjecture, we show tight or nearly tig...

• Type: Conference
• Year: 2004
• Where: FOCS
• Authors: Subhash Khot, Guy Kindler, Elchanan Mossel, Ryan O'Donnell
• Keywords: Approximation, FOCS 2004, Theoretical Computer Science, Unique Game, Unique Games Conjecture