# Sum-of-squares Lower Bounds for Planted Clique

@article{Meka2013SumofsquaresLB,
title={Sum-of-squares Lower Bounds for Planted Clique},
author={Raghu Meka and Aaron Potechin and A. Wigderson},
journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
year={2013}
}
• Published 2013
• Computer Science, Mathematics
• Proceedings of the forty-seventh annual ACM symposium on Theory of Computing
Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k = Θ(√n). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-Of-Squares hierarchy. We prove the first average case lower bound for this model: for… Expand

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