[Colloquium] [Staff] Theory Seminars at Computer Science

[Donna Brooms]

~REMINDER~

THEORY SEMINAR

November 27, 2012

3:00 p.m.

Ryerson 251

 

Pratik Worah

University of Chicago

www.cs.uchicago.edu/people/pworah

 
Title: The Complexity of Somewhat Approximation Resistant Predicates
 

Abstract: A boolean predicate $f:\{0,1\}^k\to\{0,1\}$ is said to be
{\em somewhat approximation resistant} if for some constant
$\tau > \frac{|f^{-1}(1)|}{2^k}$, given a $\tau$-satisfiable
instance of the MAX-$k$-CSP$(f)$ problem, it is NP-hard to find an
assignment that {\it strictly beats} the naive algorithm that
outputs a uniformly random assignment. Let $\tau(f)$ denote the
supremum over all $\tau$ for which this holds.
It is known that a predicate is somewhat approximation resistant
precisely when its Fourier degree is at least $3$.
For such predicates, we give a characterization
of the {\it hardness gap} $(\tau(f) - \frac{|f^{-1}(1)|}{2^k})$ up to
a factor of $O(k^5)$.
We also give a similar characterization of the {\it integrality gap}
for the natural SDP relaxation of MAX-$k$-CSP$(f)$ after $\Omega(n)$
rounds of the Lasserre hierarchy.

Joint work with Subhash Khot (NYU and U. of Chicago) and

Madhur Tulsiani (TTI Chicago).

*Refreshments will be served prior to the talk at 2:30 in Ryerson 255*

 

 

 
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