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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.
Bonnie Berger and Peter W. Shor, Approximation alogorithms for the maximum acyclic subgraph problem , Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms (Philadelphia, PA, USA), SODA ’90, Society for Industrial and Applied Mathematics, 1990, pp. 236–243
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Johan Håstad and S. Venkatesh, On the advantage over a random assignment , Random Structures Algorithms 25
2004
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Irit Dinur, Ehud Friedgut, Guy Kindler, and Ryan O’Donnell, On the Fourier tails of bounded functions over the discrete cube , Israel J. Math. 160
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Subhash Khot and Assaf Naor, Linear equations modulo 2 and the L 1 L_{1} diameter of convex bodies , SIAM J. Comput. 38
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Venkatesan Guruswami and Yuan Zhou, Approximating bounded occurrence ordering csps , Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (Anupam Gupta, Klaus Jansen, José Rolim, and Rocco Servedio, eds.), Lecture Notes in Computer Science, vol. 7408, Springer Berlin Heidelberg, 2012, pp. 158–169 (English)
2012
Cited alongside, same era.
Konstantin Makarychev, Local search is better than random assignment for bounded occurrence ordering k-csps , 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013, February 27 - March 2, 2013, Kiel, Germany, 2013, pp. 139–147
2013
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2014
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Ryan O’Donnell, Analysis of Boolean functions , Cambridge University Press, 2014
2014
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