Distributed Discovery of Large NearCliques
Abstract
Given an undirected graph and $0\le\epsilon\le1$, a set of nodes is called $\epsilon$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 nearclique. Specifically, we present a constanttime 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 $n^{\Omega(1)}$ in $O(\log n)$ time, and the algorithm also works if the graph contains a clique of size $\Omega(n/\log^{\alpha}\log n)$ for some $\alpha \in (0,1)$.
 Publication:

arXiv eprints
 Pub Date:
 May 2009
 arXiv:
 arXiv:0905.4147
 Bibcode:
 2009arXiv0905.4147B
 Keywords:

 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 C.2.4;
 F.2.2;
 G.2.2