# Beating the random assignment on constraint satisfaction problems of bounded degree

11 Aug 2015 Barak Boaz Moitra Ankur O'Donnell Ryan Raghavendra Prasad Regev Oded Steurer David Trevisan Luca Vijayaraghavan Aravindan Witmer David Wright John

We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of 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 \emph{quantum} algorithm to find an assignment satisfying a $\frac{1}{2} + \Omega(D^{-3/4})$ fraction of the equations... (read more)

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• COMPUTATIONAL COMPLEXITY
• DATA STRUCTURES AND ALGORITHMS