Kik M., Kutyłowski M., Stachowiak G. (1994) Periodic constant depth sorting networks. In: Enjalbert P., Mayr E.W., Wagner K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg
Comparator networks of constant depth can be used for sorting in the following way. The computation consists of a number of iterations, say t, each iteration being a single run through the comparator network. The output of iteration j (j < t) is used as the input for iteration j+1. The output of the iteration t is the output of the computation. In such a way, it is possible to apply a network with a small number of comparators for sorting long input sequences. However, it is not clear how to make such a computation fast.
Odd-Even Transposition Sort gives a periodic sorting network of depth 2, that sorts n numbers in n/2 iterations. The network of depth 8 proposed by Schwiegelshohn  sorts n numbers in O(√nlog n) iterations. Krammer
For a fixed but arbitrary k ∃ ℕ, we present a periodic sorting network of depth O(k) that sorts n input numbers in O(k2 · n1/k) steps.