  We present a protocol for the Boolean matrix product of two $n\times b$
Boolean matrices on the congested clique designed for the situation when the
rows of the first matrix or the columns of the second matrix are highly
clustered in the space $\{0,1\}^n.$ With high probability (w.h.p), it uses
$\tilde{O}\left(\sqrt {\frac M n+1}\right)$ rounds on the congested clique with
$n$ nodes, where $M$ is the minimum of the cost of a minimum spanning tree
(MST) of the rows of the first input matrix and the cost of an MST of the
columns of the second input matrix in the Hamming space $\{0,1\}^n.$ A key step
in our protocol is the computation of an approximate minimum spanning tree of a
set of $n$ points in the space $\{0,1\}^n$. We provide a protocol for this
problem (of interest in its own rights) based on a known randomized technique
of dimension reduction in Hamming spaces. W.h.p., it constructs an
$O(1)$-factor approximation of an MST of $n$ points in the Hamming space $\{
0,\ 1\}^n$ using $O(\log^3 n)$ rounds on the congested clique with $n$ nodes.
