Distributed discovery of large near-cliques

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.