  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 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
$n^{-\Omega(1)}$ 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 $\alpha \in
(0,1)$.
