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Revision #1 to TR13-146 | 12th April 2014 01:05

A Characterization of Approximation Resistance


Revision #1
Authors: Subhash Khot, Madhur Tulsiani, Pratik Worah
Accepted on: 12th April 2014 01:05
Downloads: 1412


This paper is withdrawn due to a bug in the trick for going from Strong Approximation Resistance to Approximation Resistance. The previous result for Strong Approximation Resistance still holds (see ECCC report TR13-075).


TR13-146 | 20th October 2013 07:35

A Characterization of Approximation Resistance

Authors: Subhash Khot, Madhur Tulsiani, Pratik Worah
Publication: 22nd October 2013 10:16
Downloads: 3322


A predicate $f:\{-1,1\}^k \mapsto \{0,1\}$ with $\rho(f) = \frac{|f^{-1}(1)|}{2^k}$ is called {\it approximation resistant} if given a near-satisfiable instance of CSP$(f)$, it is computationally hard to find an assignment that satisfies at least $\rho(f)+\Omega(1)$ fraction of the constraints.

We present a complete characterization of approximation resistant predicates under the Unique Games Conjecture. We also present characterizations in the {\it mixed} linear and semi-definite programming hierarchy and the Sherali-Adams linear programming hierarchy. In the former case, the characterization coincides with the one based on UGC. Each of the two characterizations is in terms of existence of a probability measure with certain symmetry properties on a natural convex polytope associated with the predicate.

This is a revised version of out previous paper which gave a characterization for a modified notion called "Strong Approximation Resistance".

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