Abstract
Given an undirected graph and 0 ≤ e ≤ 1, a set of nodes is called e-near clique if all but an e 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-near clique if there exists an e3-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) in O(log n) time, and the algorithm also works if the graph contains a clique of size Ω(n/logα 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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