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In computer science, a monotone priority queue is a variant of the priority queue abstract data type in which the priorities of extracted items are required to form a monotonic sequence. That is, for a priority queue in which each successively extracted item is the one with the minimum priority , the minimum priority should be monotonically increasing. Conversely for a max-heap the maximum priority should be monotonically decreasing. The assumption of monotonicity arises naturally in several applications of priority queues, and can be used as a simplifying assumption to speed up certain types of priority queues.
A necessary and sufficient condition on a monotone priority queue is that one never attempts to add an element with lower priority than the most recently extracted one.