  We consider labeling nodes of a directed graph for reachability queries. A
reachability labeling scheme for such a graph assigns a binary string, called a
label, to each node. Then, given the labels of nodes $u$ and $v$ and no other
information about the underlying graph, it should be possible to determine
whether there exists a directed path from $u$ to $v$. By a simple information
theoretical argument and invoking the bound on the number of partial orders, in
any scheme some labels need to consist of at least $n/4$ bits, where $n$ is the
number of nodes. On the other hand, it is not hard to design a scheme with
labels consisting of $n/2+O(\log n)$ bits. In the classical centralised
setting, Munro and Nicholson designed a data structure for reachability queries
consisting of $n^2/4+o(n^2)$ bits (which is optimal, up to the lower order
term). We extend their approach to obtain a scheme with labels consisting of
$n/3+o(n)$ bits.
