Distributed discovery of large near-cliques

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 in O(logn) time factor, and the algorithm also works if the graph contains a clique of size for some α (0,1). Our approach is based on a new idea of adapting property testing algorithms to the distributed setting. © 2009 Springer Berlin Heidelberg.