## Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree

##### Author(s)

Barak, Boaz; O'Donnell, Ryan; Raghavendra, Prasad; Regev, Oded; Steurer, David; Trevisan, Luca; Vijayaraghavan, Aravindan; Witmer, David; Wright, John; Moitra, Ankur; ... Show more Show less
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We show that for any odd k and any instance I of the max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a 1/2 + Omega(1/sqrt(D)) fraction of I's constraints, where D is a bound on the number of constraints that each variable occurs in. This improves both qualitatively and quantitatively on the recent work of Farhi, Goldstone, and Gutmann (2014), which gave a quantum algorithm to find an assignment satisfying a 1/2 Omega(D^{-3/4}) fraction of the equations. For arbitrary constraint satisfaction problems, we give a similar result for "triangle-free" instances; i.e., an efficient algorithm that finds an assignment satisfying at least a mu + Omega(1/sqrt(degree)) fraction of constraints, where mu is the fraction that would be satisfied by a uniformly random assignment.

##### Date issued

2015-08##### Department

Massachusetts Institute of Technology. Department of Mathematics##### Journal

Leibniz International Proceedings in Informatics

##### Publisher

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

##### Citation

Barak, Boaz et al. “Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree.” Leibniz International Proceedings in Informatics 40 (2015): n. pag.

Version: Final published version

##### ISSN

1868-8969