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On the Approximation Resistance of a Random Predicate
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0002-5379-345X
2009 (English)In: Computational Complexity, ISSN 1016-3328, E-ISSN 1420-8954, Vol. 18, no 3, 413-434 p.Article in journal (Refereed) Published
Abstract [en]

A predicate is called approximation resistant if it is NP-hard to approximate the corresponding constraint satisfaction problem significantly better than what is achieved by the naive algorithm that picks an assignment uniformly at random. In this paper we study predicates of Boolean inputs where the width of the predicate is allowed to grow. Samorodnitsky and Trevisan proved that, assuming the Unique Games Conjecture, there is a family of very sparse predicates that are approximation resistant. We prove that, under the same conjecture, any predicate implied by their predicate remains approximation resistant and that, with high probability, this condition applies to a randomly chosen predicate.

Place, publisher, year, edition, pages
2009. Vol. 18, no 3, 413-434 p.
Keyword [en]
Constraint satisfaction problem, approximation algorithms, approximation resistance
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-18882DOI: 10.1007/s00037-009-0262-8ISI: 000270979800003ScopusID: 2-s2.0-71549164098OAI: diva2:336929

QC 20100525

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-09-25Bibliographically approved

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Håstad, Johan
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