ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 0905.4147
90
0

Distributed Discovery of Large Near-Cliques

26 May 2009
Zvika Brakerski
Boaz Patt-Shamir
    GNN
ArXiv (abs)PDFHTML
Abstract

Given an undirected graph and 0≤ϵ≤10\le\epsilon\le10≤ϵ≤1, a set of nodes is called ϵ\epsilonϵ-near clique if all but an ϵ\epsilonϵ fraction of the pairs of nodes in the set have a link between them. In this paper we present a fast synchronous network algorithm that uses small messages and finds a near-clique. Specifically, we present a constant-time algorithm that finds, with constant probability of success, a linear size ϵ\epsilonϵ-near clique if there exists an ϵ3\epsilon^3ϵ3-near clique of linear size in the graph. The algorithm uses messages of O(log⁡n)O(\log n)O(logn) bits. The failure probability can be reduced to n−Ω(1)n^{-\Omega(1)}n−Ω(1) in O(log⁡n)O(\log n)O(logn) time, and the algorithm also works if the graph contains a clique of size Ω(n/log⁡αlog⁡n)\Omega(n/\log^{\alpha}\log n)Ω(n/logαlogn) for some α∈(0,1)\alpha \in (0,1)α∈(0,1).

View on arXiv
Comments on this paper