Approximation Resistant Predicates from Pairwise Independence
Austrin, P.
Mossel, E.
R. Inst. of Technol., KTH, Stockholm;
This paper appears in: Computational Complexity, 2008. CCC '08. 23rd Annual IEEE Conference on
Publication Date: 23-26 June 2008
On page(s): 249-258
Location: College Park, MD,
ISSN: 1093-0159
ISBN: 978-0-7695-3169-4
INSPEC Accession Number: 10074109
Digital Object Identifier: 10.1109/CCC.2008.20
Current Version Published: 2008-07-09
Abstract
We study the approximability of predicates on k variables from a domain [q], and give a new sufficient condition for such predicates to be approximation resistant under the unique games conjecture. Specifically, we show that a predicate P is approximation resistant if there exists a balanced pairwise independent distribution over [q]k whose support is contained in the set of satisfying assignments to P. Using constructions of pairwise independent distributions this result implies that ldr For general kges3 and qges2, the MAX k-CSPq problem is UG-hard to approximate within O(kq2)/qk+isin. ldr For the special case of q=2, i.e., boolean variables, we can sharpen this bound to (k+O(k0.525))/2k+isin, improving upon the best previous bound of2k/2k+isin (Samorodnitsky and Trevisan, STOC'06) by essentially a factor 2. ldr Finally, again for q=2, assuming that the famous Hadamard conjecture is true, this can be improved even further, and the O(k0.525) term can be replaced by the constant 4.
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