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A priority queue is an abstract data type in computer programming, supporting the following three operations:

  • add an element to the queue with an associated priority
  • remove the element from the queue that has the highest priority, and return it
  • (optionally) peek at the element with highest priority without removing it

The simplest way to implement a priority queue data type is to keep an associative array mapping each priority to a list of elements with that priority. If association lists are used to implement the associative array, adding an element takes constant time but removing or peeking at the element of highest priority takes linear (O(n)) time, because we must search all keys for the largest one. If a self-balancing binary search tree is used, all three operations take O(log n) time; this is a popular solution in environments that already provide balanced trees but nothing more sophisticated. The van Emde Boas tree, another associative array data structure, can perform all three operations in O(log log n) time, but at a space cost for small queues of about O(2m/2), where m is the number of bits in the priority value, which may be prohibitive.

There are a number of specialized heap data structures that either supply additional operations or outperform the above approaches. The binary heap uses O(log n) time for both operations, but allows peeking at the element of highest priority without removing it in constant time. Binomial heaps add several more operations, but require O(log n) time for peeking. Fibonacci heaps can insert elements, peek at the maximum priority element, and increase an element's priority in amortized constant time (deletions are still O(log n)).

The Standard Template Library (STL), part of the C++ 1998 standard, specifies "priority_queue" as one of the STL container adaptor class templates. Unlike actual STL containers, it does not allow iteration of its elements (it strictly adheres to its abstract data type definition). Java's library contains a PriorityQueue class.

Applications

Bandwidth management

Priority queuing can be used to manage limited resources such as bandwidth on a transmission line from a network router. In the event of outgoing traffic queuing due to insufficient bandwidth, all other queues can be halted to send the traffic from the highest priority queue upon arrival. This ensures that the prioritized traffic (such as real-time traffic, e.g. a RTP stream of a VoIP connection) is forwarded with the least delay and the least likelihood of being rejected due to a queue reaching its maximum capacity. All other traffic can be handled when the highest priority queue is empty. Another approach used is to send disproportionately more traffic from higher priority queues.

Usually a limitation (policer) is set to limit the bandwidth that traffic from the highest priority queue can take, in order to prevent high priority packets from choking off all other traffic. This limit is usually never reached due to high lever control instances such as the Cisco Callmanager, which can be programmed to inhibit calls which would exceed the programmed bandwidth limit.

Discrete event simulation

Another use of a priority queue is to manage the events in a discrete event simulation. The events are added to the queue with their simulation time used as the priority. The execution of the simulation proceeds by repeatedly pulling the top of the queue and executing the event thereon.

See also: Scheduling (computing), queueing theory

A* search algorithm

The A* search algorithm finds the shortest path between two vertices of a weighted graph, trying out the most promising routes first. The priority queue is used to keep track of unexplored routes; the one for which a lower bound on the total path length is smallest is given highest priority.

Implementations

While relying on heapsort is a common way to implement priority queues, for integer data faster implementations exist.

  • When the set of keys is {1, 2, ..., C}, a data structure by Emde Boas supports the minimum, maximum, insert, delete, search, extract-min, extract-max, predecessor and successor operations in O(log C) time.

An algorithm by Fredman and Willard implements the minimum operation in O(1) time and insert and extract-min operations in time.

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Source:  OpenStax, Data structures and algorithms. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10765/1.1
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