Abstract
In this article, we study the approximability of satisfiable Max 3CSP-q for q > 3 be a prime. We give a \((\frac{1}{q}+\frac{1}{q^2}-\frac{1}{q^3})+\epsilon\)-hardness result for approximate Max 3CSP-q even on satisfiable instances, conditioned on Khot’s d-to-1 Conjecture, for any finite constant integer d < q/2.
This work is supported by Hundred Talent Program of Chinese Academy of Sciences under Angsheng Li.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Austrin, P., Mossel, E.: Approximation Resistant Predicates From Pairwise Independence. ECCC TR08-009 (2008)
Charikar, M., Makarychev, K., Makarychev, Y.: Near-Optimal Algorithms for Unique Games. In: Proceedings of the 38-th Annual ACM Symposium on Theory of Computing, pp. 205–214 (2006)
Charikar, M., Makarychev, K., Makarychev, Y.: Near-Optimal Algorithms for Maximum Constraint Satisfaction Problems. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 62–68 (2007)
Engebretsen, L., Holmerin, J.: Three-query PCPs with perfect completeness over non-Boolean domains. Random Structures and Algorithms 27(1), 46–75 (2005)
Håstad, J.: Some optimal inapproximability reaults. J.ACM 48(4), 798–859 (2001)
Khot, S.: On the power of unique 2-pover 1-round games. In: Proceedings of 34th ACM Symposium on Theory of Computating, pp. 767–775 (2002)
Khot, S., Kindler, G., Mossel, E., Donnell, R.: Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs? In: Proceedings of 45th Annual IEEE Symposium of Foundations of Computer Science, pp. 146–154 (2004)
Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2 − ε. In: Proceedings of 18th IEEE Conference on Computational Complexity, pp. 379–386 (2003)
Mossel, E.: Gaussian bounds for noise correlation of functions. arXiv Report math/0703683v3 (2007)
Mossel, E., Donnell, R., Oleszkiewicz, K.: Noise stability of functions with low influences:invariance and optimality. In: Proceedings of 48th Annual IEEE Symposium of Foundations of Computer Science, pp. 307–317 (2007)
O’Donnell, R., Wu, Y.: Conditional hardness for satisfiable 3-CSPs. In: Proceedings of the 41-th Annual ACM Symposium on Theory of Computing, pp. 493–502 (2009)
Oleszkiewicz, K.: On a nonsymmetric version of the Khinchine-Kahane inequality. Progress in Probability 56, 156–168 (2003)
Raghavendra, P.: Optimal Algorithms and Inapproximability Results for Every CSP? In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing (to appear) (2008)
Wollf, P.: Hypercontractivity of simple random variables. In: The 46th Annual Symposium on Foundations of Computer Science, pp. 740–746 (2005)
Zwick, U.: Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 201–210 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tang, L. (2009). Conditional Hardness of Approximating Satisfiable Max 3CSP-q . In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_93
Download citation
DOI: https://doi.org/10.1007/978-3-642-10631-6_93
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10630-9
Online ISBN: 978-3-642-10631-6
eBook Packages: Computer ScienceComputer Science (R0)