A method of constructing selection networks with O(log n) depth

A classifier with n inputs is a comparator network that classifies a set of n values into two classes with the same number of values in such a way that each value in one class is at least as large as all of those in the other. Based on the utilization of expanders, Pippenger constructed classifiers with n inputs whose size is asymptotic to 2n log₂ n. In the same spirit, we obtain a relatively simple method of constructing classifiers of depth O(log n). Consequently, for an arbitrary constant C > 3/log₂ 3 = 1.8927 . . ., we construct classifiers of depth O(log n) and of size at most Cn log₂ n + O(n).