# priority queue

(data structure)

**Definition:**
An *abstract data type* to efficiently support finding the item with the highest priority across a series of operations. The basic operations are: insert, find-minimum (or maximum), and delete-minimum (or maximum). Some implementations also efficiently support join two priority queues (*meld*), delete an arbitrary item, and increase the priority of a item (decrease-key).

**Formal Definition:** The operations new(), insert(v, PQ), find-minimum or min(PQ), and delete-minimum or dm(PQ) may be defined with *axiomatic semantics* as follows.

- new() returns a priority queue
- min(insert(v, new())) = v
- dm(insert(v, new())) = new()
- min(insert(v, insert(w, PQ))) = if priority(v) < priority(min(insert(w, PQ))) then v else min(insert(w, PQ))
- dm(insert(v, insert(w, PQ))) = if priority(v) < priority(min(insert(w, PQ))) then insert(w, PQ) else insert(v, dm(insert(w, PQ)))

where PQ is a priority queue, v and w are items, and priority(v) is the priority of item v.
**Generalization** (I am a kind of ...)

*abstract data type*.

**Specialization** (... is a kind of me.)

*pagoda*, *leftist tree*, *van Emde-Boas priority queue*.

**Aggregate parent** (I am a part of or used in ...)

*best-first search*, *Dijkstra's algorithm*.

**Aggregate child** (... is a part of or used in me.)

*heap*, *Fibonacci heap*.

**See also**
*discrete interval encoding tree*, *hash heap*, *calendar queue*, *queue*.

*Note:
It can be implemented efficiently with a **heap*. After LK.

Author: PEB

## Implementation

Links to implementations, dozens of papers, introductory material, etc..

Go to the
Dictionary of Algorithms and Data
Structures home page.

If you have suggestions, corrections, or comments, please get in touch
with Paul Black.

Entry modified 22 November 2021.

HTML page formatted Mon Nov 22 06:32:06 2021.

Cite this as:

Paul E. Black, "priority queue", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 22 November 2021. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/priorityque.html