Perfect and separating Hash families: new bounds via the algorithmic   cluster expansion local lemma
  We present new lower bounds for the size of perfect and separating hash families ensuring their existence. Such new bounds are based on the algorithmic Cluster expansion improved version of the Lov\'asz Local Lemma, which also implies that the Moser-Tardos algorithm finds such hash families in polynomial time. 
Aldo Procacci and Remy Sanchis
math.CO