@inproceedings{26c20cf922794e39809782d0e8864d4c,
title = "Finding hidden cliques in linear time with high probability",
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(n2). 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(n2), and has a failure probability that is less than polynomially small.",
author = "Yael Dekel and Ori Gurel-Gurevich and Yuval Peres",
note = "Publisher Copyright: {\textcopyright} Copyright (2011) by SIAM: Society for Industrial and Applied Mathematics. All rights reserved.; 8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011 ; Conference date: 22-01-2011",
year = "2011",
doi = "https://doi.org/10.1137/1.9781611973013.8",
language = "الإنجليزيّة",
series = "8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011",
publisher = "Society for Industrial and Applied Mathematics Publications",
pages = "67--75",
booktitle = "8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011",
address = "الولايات المتّحدة",
}