Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Linear lower bound on degrees of positivstellensatz calculus proofs for the parity
Theoretical Computer Science
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
A Fourier-theoretic perspective on the Condorcet paradox and Arrow's theorem
Advances in Applied Mathematics
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
An optimal sdp algorithm for max-cut, and equally optimal long code tests
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Improved Approximation Guarantees through Higher Levels of SDP Hierarchies
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Linear Level Lasserre Lower Bounds for Certain k-CSPs
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Elections Can be Manipulated Often
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
SDP Integrality Gaps with Local ell_1-Embeddability
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approximate Lasserre integrality gap for unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Rounding Semidefinite Programming Hierarchies via Global Correlation
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Hypercontractivity, sum-of-squares proofs, and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Gaussian Noise Sensitivity and Fourier Tails
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
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The Majority is Stablest Theorem has numerous applications in hardness of approximation and social choice theory. We give a new proof of the Majority is Stablest Theorem by induction on the dimension of the discrete cube. Unlike the previous proof, it uses neither the "invariance principle" nor Borell's result in Gaussian space. The new proof is general enough to include all previous variants of majority is stablest such as "it ain't over until it's over" and "Majority is most predictable". Moreover, the new proof allows us to derive a proof of Majority is Stablest in a constant level of the Sum of Squares hierarchy. This implies in particular that Khot-Vishnoi instance of Max-Cut does not provide a gap instance for the Lasserre hierarchy.