### Abstract

We consider the following probabilistic model of a graph on n labeled vertices. First choose a random graph G(n, 1/2) and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for various values of k. This question was posed independently, in various variants, by Jerrum and by Kucera. In this paper we present an efficient algorithm for all k>cn^{0.5}, for any fixed c>0, thus improving the trivial case k>cn^{0.5} (log n)^{0.5}. The algorithm is based on the spectral properties of the graph.

Original language | English (US) |
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Pages | 594-598 |

Number of pages | 5 |

State | Published - Dec 1 1998 |

Externally published | Yes |

Event | Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA Duration: Jan 25 1998 → Jan 27 1998 |

### Other

Other | Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms |
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City | San Francisco, CA, USA |

Period | 1/25/98 → 1/27/98 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

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## Cite this

*Finding a large hidden clique in a random graph*. 594-598. Paper presented at Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms, San Francisco, CA, USA, .