An efficient implementation of priority queues where insert, delete, get minimum, get maximum, etc. take O(log log N) time, where N is the total possible number of keys. Depending on the circumstance, the implementation is null (if the queue is empty), an integer (if the queue has one integer), a bit vector of size N (if N is small), or a special data structure: an array of priority queues, called the bottom queues, and one more priority queue of array indexes of the bottom queues.