Guy Kindler

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

Approximating-CVP to within almost-polynomial factors is NP-hard

\alpha_{\text{\tiny{GW}}} + \epsilon

Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors

for all

Optimal inapproximability results for MAX-CUT and other 2-variable CSPs?

\epsilon > 0

Testing juntas

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On non-approximability for quadratic programs

\alpha_{\text{\tiny{GW}}} \approx .878567

The geometry of manipulation — A quantitative proof of the Gibbard-Satterthwaite theorem

denotes the approximation ratio achieved by the algorithm of Goemans and Williamson in [J. Assoc. Comput. Mach., 42 (1995), pp. 1115-1145]. This implies that if the Unique Games Conjecture of Khot in [Proceedings of the 34th Annual ACM Symposium on Theory of Computing, 2002, pp. 767-775] 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 [E. Mossel, R. O’Donnell, and K. Oleszkiewicz, Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, 2005, pp. 21-30]. A stronger version of this conjecture called Plurality Is Stablest is still open, although [E. Mossel, R. O’Donnell, and K. Oleszkiewicz, Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, 2005, pp. 21-30] 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 tight hardness results for MAX-2SAT, MAX-

PCP characterizations of NP: towards a polynomially-small error-probability

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Simulating independence: New constructions of condensers, ramsey graphs, dispersers, and extractors

-CUT, and MAX-2LIN(

Lower Bounds for the Noisy Broadcast Problem

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