# Finding Planted Cliques in Sublinear Time

@article{Mardia2020FindingPC, title={Finding Planted Cliques in Sublinear Time}, author={Jay Mardia and Hilal Asi and Kabir Chandrasekher}, journal={ArXiv}, year={2020}, volume={abs/2004.12002} }

We study the planted clique problem in which a clique of size $k$ is planted in an Erdős-Renyi graph of size $n$ and one wants to recover this planted clique. For $k=\Omega(\sqrt{n})$, polynomial time algorithms can find the planted clique. The fastest such algorithms run in time linear $O(n^2)$ (or nearly linear) in the size of the input [FR10,DGGP14,DM15a]. In this work, we develop sublinear time algorithms that find the planted clique when $k=\omega(\sqrt{n \log \log n})$. Our algorithms can… CONTINUE READING

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