Distributed discovery of large near-cliques |
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Authors: | Zvika Brakerski Boaz Patt-Shamir |
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Affiliation: | 1. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel 2. Department of Electrical Engineering, Tel Aviv University, 69978, Tel Aviv, Israel
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Abstract: | Given an undirected graph and 0 £ e £ 1{0leepsilonle1}, a set of nodes is called an e{epsilon}-near clique if all but an e{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 e{epsilon}-near clique if there exists an e3{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 a ? (0,1){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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