  In this paper we extend the knowledge on the problem of empirically searching
for sorting networks of minimal depth. We present new search space pruning
techniques for the last four levels of a candidate sorting network by
considering only the output set representation of a network. We present an
algorithm for checking whether an $n$-input sorting network of depth $d$ exists
by considering the minimal up to permutation and reflection itemsets at each
level and using the pruning at the last four levels. We experimentally
evaluated this algorithm to find the optimal depth sorting networks for all $n
\leq 12$.
