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 $2n\log_{2}n$. In the same spirit, we obtain a relatively simple method to construct classifiers of depth $O(\log n)$. In consequence, for arbitrary constant $C > 3/\log_2 3 = 1.8927\cdots$, we construct classifiers of depth $O(\log n)$ and of size at most $Cn\log_{2}n + O(n)$.