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Distributed Discovery of Large Near-Cliques

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Book cover Distributed Computing (DISC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5805))

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Abstract

Given an undirected graph and 0 ≤ ε ≤ 1, a set of nodes is called ε-near clique if all but an ε 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-near clique if there exists an ε 3-near clique of linear size in the graph. The algorithm uses messages of O(logn) bits. The failure probability can be reduced to \(n^{-{\it \Omega}(1)}\) in O(logn) time factor, and the algorithm also works if the graph contains a clique of size \({\it \Omega}(n/\log^{\alpha}\log n)\) for some α ∈ (0,1). Our approach is based on a new idea of adapting property testing algorithms to the distributed setting.

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Author information

Authors and Affiliations

  1. Weizmann Institute of Science, Israel

    Zvika Brakerski

  2. Dept. of Electrical Engineering, Tel-Aviv University, Israel

    Boaz Patt-Shamir

Authors
  1. Zvika Brakerski
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  2. Boaz Patt-Shamir
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Idit Keidar

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Brakerski, Z., Patt-Shamir, B. (2009). Distributed Discovery of Large Near-Cliques. In: Keidar, I. (eds) Distributed Computing. DISC 2009. Lecture Notes in Computer Science, vol 5805. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04355-0_22

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  • DOI: https://doi.org/10.1007/978-3-642-04355-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04354-3

  • Online ISBN: 978-3-642-04355-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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