Distributed discovery of large near-cliques

作者：Brakerski Zvika; Patt Shamir Boaz^*

来源：Distributed Computing, 2011, 24(2): 79-89.

DOI：10.1007/s00446-011-0132-x

Given an undirected graph and 0 <= epsilon <= 1, 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(-Omega(1)) by increasing the time complexity by a logarithmic factor, and the algorithm also works if the graph contains a clique of size Omega(n/(log log n)(alpha)) for some alpha is an element of (0, 1). Our approach is based on a new idea of adapting property testing algorithms to the distributed setting.

• 出版日期2011-10