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Distributed discovery of large near-cliques

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Abstract

Given an undirected graph and \({0\le\epsilon\le1}\), a set of nodes is called an \({\epsilon}\)-near clique if all but an \({\epsilon}\) 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 \({\epsilon}\)-near clique if there exists an \({\epsilon^3}\)-near clique of linear size in the graph. The algorithm uses messages of O(log n) bits. The failure probability can be reduced to n −Ω(1) by increasing the time complexity by a logarithmic factor, and the algorithm also works if the graph contains a clique of size Ω(n/(log log n)α) for some \({\alpha \in (0,1)}\). Our approach is based on a new idea of adapting property testing algorithms to the distributed setting.

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Authors and Affiliations

  1. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel

    Zvika Brakerski

  2. Department of Electrical Engineering, Tel Aviv University, 69978, Tel Aviv, Israel

    Boaz Patt-Shamir

Authors
  1. Zvika Brakerski
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  2. Boaz Patt-Shamir
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Corresponding author

Correspondence to Boaz Patt-Shamir.

Additional information

B. Patt-Shamir was supported in part by the Israel Science Foundation grant 1372/09, and by Israel Ministry of Science and Technology.

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Brakerski, Z., Patt-Shamir, B. Distributed discovery of large near-cliques. Distrib. Comput. 24, 79–89 (2011). https://doi.org/10.1007/s00446-011-0132-x

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  • DOI: https://doi.org/10.1007/s00446-011-0132-x

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