Before revision:  This implies the existence of a reachability labelling scheme for digraphs with labels of n/4+o(n) bits per vertex . We also use this result to construct a poset on 2^{n/4+o(n) . All these results are best possible, up to the lower order term , and solve several open problems in the area .
After revision:  This implies the existence of a reachability labelling scheme for digraphs with labels of n/4+o(n) bits per vertex and comparability labelling scheme for posets with labels of n/4+o(n) bits per element . All these results are best possible, up to the lower order term , and solve several open problems in the area .