Is there a sorting network of depth $\text{O}(\log n)$ for selecting the $i$th order statistic?Remark: I've already asked a related question in a different context.  Although the two questions are related, this is not a duplicate of the other one.
Selection algorithm on depth-$\text{O}(\log n)$ sorting network
dc.parallel comp;sorting;sorting network
You can construct selection networks of depth O(log n) using graph expanders or using variants of the AKS sorting network.S. Jimbo and A. Maruoka, A Method of Constructing Selection Networks with $O(\log n)$ Depth,SIAM J. Comput. 25, pp. 709-739, http://dx.doi.org/10.1137/S0097539793248329