Priority queue with dynamic item priorities

Question

I need to implement a priority queue where the priority of an item in the queue can change and the queue adjusts itself so that items are always removed in the correct order. I have some ideas of how I could implement this but I'm sure this is quite a common data structure so I'm hoping I can use an implementation by someone smarter than me as a base.

Can anyone tell me the name of this type of priority queue so I know what to search for or, even better, point me to an implementation?

Answer 1

Priority queues such as this are typically implemented using a binary heap data structure as someone else suggested, which usually is represented using an array but could also use a binary tree. It actually is not hard to increase or decrease the priority of an element in the heap. If you know you are changing the priority of many elements before the next element is popped from the queue you can temporarily turn off dynamic reordering, insert all of the elements at the end of the heap, and then reorder the entire heap (at a cost of O(n)) just before the element needs to be popped. The important thing about heaps is that it only costs O(n) to put an array into heap order but O(n log n) to sort it.

I have used this approach successfully in a large project with dynamic priorities.

Here is my implementation of a parameterized priority queue implementation in the Curl programming language.

Answer 2

A standard binary heap supports 5 operations (the example below assume a max heap):

* find-max: return the maximum node of the heap
* delete-max: removing the root node of the heap
* increase-key: updating a key within the heap
* insert: adding a new key to the heap
* merge: joining two heaps to form a valid new heap containing all the elements of both.

As you can see, in a max heap, you can increase an arbitrary key. In a min heap you can decrease an arbitrary key. You can't change keys both ways unfortunately, but will this do? If you need to change keys both ways then you might want to think about using a a min-max-heap.