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SoS and Planted Clique: Tight Analysis of MPW Moments at all Degrees and an Optimal Lower Bound at Degree Four
[article]
2015
arXiv
pre-print
The problem of finding large cliques in random graphs and its "planted" variant, where one wants to recover a clique of size $\omega \gg \log{(n)}$ added to an \Erdos-\Renyi graph $G \sim G(n,\frac{1}{2})$, have been intensely studied. Nevertheless, existing polynomial time algorithms can only recover planted cliques of size $\omega = \Omega(\sqrt{n})$. By contrast, information theoretically, one can recover planted cliques so long as $\omega \gg \log{(n)}$. In this work, we continue the
arXiv:1507.05230v1
fatcat:ilfntzjljbdo3cdu6xetaox3v4