The asymptotic complexity of partial sorting -- How to learn large   posets by pairwise comparisons
  The expected number of pairwise comparisons needed to learn a partial order on n elements is shown to be at least n*n/4-o(n*n), and an algorithm is given that needs only n*n/4+o(n*n) comparisons on average. In addition, the optimal strategy for learning a poset with four elements is presented. 
Jobst Heitzig