A maximum priority queue is an abstract data type holding items with comparable priority keys and giving access to a greatest-key item. Equal priorities may occur; any one of the tied maximum items can be returned unless a tie rule is specified.
  • empty or initialization creates a queue with no items; isEmpty and size inspect its occupancy.
  • insert(item, key) adds an item with its priority.
  • maximum() returns a greatest-priority item without removing it.
  • extractMax() returns and removes a greatest-priority item.
  • When mutable priorities are supported, increaseKey(handle, newKey) raises an existing item's priority; the handle identifies its stored location.
The central behavior is . Calling maximum or extractMax on an empty queue must report that no item exists. Raising a key is a common supported extension; arbitrary-key changes and deletion by handle can also be supplied.

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