Before revision:  By now, we have quite fast algorithms---usually sublogarithimic-time and often \text{poly (\log\log n)-time, or even faster---for a number of fundamental graph problems in the massively parallel computation (MPC) model.
After revision:  By now, we have quite fast algorithms---usually sublogarithmic-time and often poly (\log\log n)-time, or even faster---for a number of fundamental graph problems in the massively parallel computation (MPC) model.