## Abstract

We are given a graph G with n vertices, where a random subset of κ vertices has been made into a clique, and the remaining edges are chosen independently with probability 1/2 This random graph model is denoted G(n,1/2,k). The hidden clique problem is to design an algorithm that finds the κ-clique in polynomial time with high probability. An algorithm due to Alon, Krivelevich and Sudakov [3] uses spectral techniques to find the hidden clique with high probability when κ = c√n for a sufficiently large constant c > 0. Recently, an algorithm that solves the same problem was proposed by Feige and Ron [14]. It has the advantages of being simpler and more intuitive, and of an improved running time of O(n^{2}). However, the analysis in [14] gives success probability of only 2/3. In this paper we present a new algorithm for finding hidden cliques that both runs in time O(n^{2}), and has a failure probability that is less than polynomially small.

Original language | American English |
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Title of host publication | 8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011 |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 67-75 |

Number of pages | 9 |

ISBN (Electronic) | 9781617823152 |

DOIs | |

State | Published - 2011 |

Externally published | Yes |

Event | 8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011 - San Francisco, United States Duration: 22 Jan 2011 → … |

### Publication series

Name | 8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011 |
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### Conference

Conference | 8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011 |
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Country/Territory | United States |

City | San Francisco |

Period | 22/01/11 → … |

### Bibliographical note

Publisher Copyright:© Copyright (2011) by SIAM: Society for Industrial and Applied Mathematics. All rights reserved.