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

Though it is unable to prove the majority is stablest conjecture, some partial results are enough to imply that MAX-CUT is hard to (3/4 + 1/(2/spl pi/) + /spl epsi/)-approximate (/spl ap/ .909155), assuming only the unique games conjecture.
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Noise stability of functions with low influences: Invariance and optimality

An invariance principle for multilinear polynomials with low influences and bounded degree is proved; it shows that under mild conditions the distribution of such polynmials is essentially invariant for all product spaces.
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Analysis of Boolean Functions

This text gives a thorough overview of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry, and includes a "highlight application" such as Arrow's theorem from economics.
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Learning juntas

The algorithm and analysis exploit new structural properties of Boolean functions and obtain the first polynomial factor improvement on the naive n-k time bound which can be achieved via exhaustive search.
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Every decision tree has an influential variable

A very easy proof that the randomized query complexity of nontrivial monotone graph properties is at least/spl Omega/(v/sup 4/3//p/sup 1/3/), where v is the number of vertices and p /spl les/ 1/2 is the critical threshold probability.
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Optimal Lower Bounds for Locality-Sensitive Hashing (Except When q is Tiny)

The “optimal” lower bound for Locality-Sensitive Hashing (LSH) must be at least 1/<i>c</i> (minus <i>o</i><sub>d</sub>(1) is shown, following almost immediately from the observation that the noise stability of a boolean function at time <i-t</i) is a log-convex function of <i*t</ i.
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Optimal mean-based algorithms for trace reconstruction

For any constant deletion rate 0 < Ω < 1, a mean-based algorithm is given that uses exp(O(n1/3) time and traces; it is proved that any mean- based algorithm must use at least exp(Ω(n 1/3)) traces; and a surprising result is found: for deletion probabilities δ > 1/2, the presence of insertions can actually help with trace reconstruction.
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Learning intersections and thresholds of halfspaces

We give the first polynomial time algorithm to learn any function of a constant number of halfspaces under the uniform distribution to within any constant error parameter. We also give the first…
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Testing Halfspaces

This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(w · x - θ) by giving an algorithm that distinguishes halfspaces from functions that are e-far from any halfspace using only poly(1/e) queries, independent of the dimension n.
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Learning Geometric Concepts via Gaussian Surface Area

Gaussian surface area essentially characterizes the computational complexity of learning under the Gaussian distribution, and this is the first subexponential time algorithm for learning general convex sets even in the noise-free (PAC) model.
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