In a system for efficiently detecting large/elephant flows in a network, the rate at which the received packets are sampled is adjusted according to the measured heavy tailedness of the arriving traffic, such that the measured heavy tailedness reaches a specified target level. The heavy tailedness is measured using the estimated sizes of different flows associated with the arriving packets. When the measured heavy tailedness reaches and remains at the specified target level, the flows having the largest estimated sizes are likely to be the largest/elephant flows in the network.