Sorting inc logn parallel steps

We give a sorting network withcn logn comparisons. The algorithm can be performed inc logn parallel steps as well, where in a parallel step we comparen/2 disjoint pairs. In thei-th step of the algorithm we compare the contents of registersRj(i), andRk(i), wherej(i), k(i) are absolute constants then change their contents or not according to the result of the comparison.

[1]  Z. Galil,et al.  Explicit constructions of linear size superconcentrators , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).