A Characterization of Approximation Resistance
نویسندگان
چکیده
A predicate f : {−1, 1} → {0, 1} with ρ(f) = |f −1(1)| 2k is called approximation resistant if given a near-satisfiable instance of CSP(f), it is computationally hard to find an assignment that satisfies at least ρ(f) + Ω(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 mixed linear and semidefinite 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. ∗NYU. [email protected] Research partly supported by NSF Expeditions grant CCF-0832795, NSF Waterman Award and BSF grant 2008059. Part of the research carried out while the author was at U.Chicago. †Toyota Technological Institute at Chicago. [email protected]. Research supported by NSF Career Award CCF-1254044. ‡NYU. [email protected] Research partly supported by Subhash Khot’s NSF Waterman Award. Part of the research carried out while the author was at U.Chicago.
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عنوان ژورنال:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 20 شماره
صفحات -
تاریخ انتشار 2013