Finding Hidden Cliques of Size √(N/e) in Nearly Linear Time

@article{Deshpande2015FindingHC,
  title={Finding Hidden Cliques of Size √(N/e) in Nearly Linear Time},
  author={Yash Deshpande and Andrea Montanari},
  journal={Foundations of Computational Mathematics},
  year={2015},
  volume={15},
  pages={1069-1128}
}
Consider an Erdös-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset CN of the vertices that form a clique (a completely connected subgraph). We consider the problem of identifying the clique, given a realization of such a random graph. The best known algorithm provably finds the clique in linear time with high probability, provided |CN | ≥ 1.261 √ N [YDP11]. Spectral methods can be shown to fail on cliques smaller than √ N . In this paper… CONTINUE READING

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