We show that in the deterministic comparison model for parallel computation, p = n processors can select the kth smallest item from a set of n numbers in O(log log n) parallel time. With this result all comparison tasks (selection, merging, sorting) now have upper and lower bounds of the same order in both random and deterministic models. This optimal time bound holds even if p = o(n). © 1989.
Ajtai, M., Komlós, J., Steiger, W. L., & Szemerédi, E. (1989). Optimal parallel selection has complexity O(Log Log N). Journal of Computer and System Sciences, 38(1), 125–133. https://doi.org/10.1016/0022-0000(89)90035-4