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Approximation resistant predicates from pairwise independence
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0001-8217-0158
2009 (English)In: Computational Complexity, ISSN 1016-3328, E-ISSN 1420-8954, Vol. 18, no 2, 249-271 p.Article in journal (Refereed) Published
Abstract [en]

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 For general k >= 3 and q <= 2, the Max k-CSPq problem is UG-hard to approximate within O(kq(2))/q(k) + epsilon. For the special case of q = 2, i.e., boolean variables, we can sharpen this bound to (k + O(k(0.525)))/2(k) + epsilon, improving upon the best previous bound of 2k/2(k) + epsilon (Samorodnitsky and Trevisan, STOC'06) by essentially a factor 2. Finally, again for q = 2, assuming that the famous Hadamard Conjecture is true, this can be improved even further, and the O(k(0.525)) term can be replaced by the constant 4.

Place, publisher, year, edition, pages
2009. Vol. 18, no 2, 249-271 p.
Keyword [en]
Approximation resistance, constraint satisfaction, unique games conjecture
National Category
Computer Science
URN: urn:nbn:se:kth:diva-30809DOI: 10.1007/s00037-009-0272-6ISI: 000267365500005ScopusID: 2-s2.0-68149178817OAI: diva2:403235

QC 20150624

Available from: 2011-03-11 Created: 2011-03-04 Last updated: 2015-06-24Bibliographically approved

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