Corpus ID: 119313669

The Landscape of the Planted Clique Problem: Dense subgraphs and the Overlap Gap Property

@article{Gamarnik2019TheLO,
  title={The Landscape of the Planted Clique Problem: Dense subgraphs and the Overlap Gap Property},
  author={D. Gamarnik and Ilias Zadik},
  journal={ArXiv},
  year={2019},
  volume={abs/1904.07174}
}
  • D. Gamarnik, Ilias Zadik
  • Published 2019
  • Computer Science, Mathematics
  • ArXiv
  • In this paper we study the computational-statistical gap of the planted clique problem, where a clique of size $k$ is planted in an Erdos Renyi graph $G(n,\frac{1}{2})$ resulting in a graph $G\left(n,\frac{1}{2},k\right)$. The goal is to recover the planted clique vertices by observing $G\left(n,\frac{1}{2},k\right)$ . It is known that the clique can be recovered as long as $k \geq \left(2+\epsilon\right)\log n $ for any $\epsilon>0$, but no polynomial-time algorithm is known for this task… CONTINUE READING
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