Finding hidden cliques in linear time with high probability

Yael Dekel, Ori Gurel-Gurevich, Yuval Peres

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

20 Scopus citations

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.

Original languageAmerican English
Title of host publication8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011
PublisherSociety for Industrial and Applied Mathematics Publications
Pages67-75
Number of pages9
ISBN (Electronic)9781617823152
DOIs
StatePublished - 2011
Externally publishedYes
Event8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011 - San Francisco, United States
Duration: 22 Jan 2011 → …

Publication series

Name8th Workshop on Analytic Algorithmics and Combinatorics 2011, ANALCO 2011

Conference

Conference8th Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2011
Country/TerritoryUnited States
CitySan Francisco
Period22/01/11 → …

Bibliographical note

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

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