On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computer assisted proof of optimal approximability results
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A dependence maximization view of clustering
Proceedings of the 24th international conference on Machine learning
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On the Unique Games Conjecture (Invited Survey)
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Sharp kernel clustering algorithms and their associated Grothendieck inequalities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Grothendieck Constant is Strictly Smaller than Krivine's Bound
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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It is shown that every measurable partition {A1,..., Ak} of R3 satisfies: ∑i=1k|intAi xe-1/2|x|22dx|22≤ 9π2. Let P1,P2,P3 be the partition of R2 into 120o sectors centered at the origin. The bound (1) is sharp, with equality holding if Ai=Pi x R for i∈ {1,2,3} and Ai=∅ for i∈ {4,...,k}. This settles positively the 3-dimensional Propeller Conjecture of Khot and Naor (FOCS 2008). The proof of (1) reduces the problem to a finite set of numerical inequalities which are then verified with full rigor in a computer-assisted fashion. The main consequence (and motivation) of (1) is complexity-theoretic: the Unique Games hardness threshold of the Kernel Clustering problem with 4 x 4 centered and spherical hypothesis matrix equals 2π/3.