Addressable heap

In computer science, an addressable heap is an abstract data type. Specifically, it is a mergeable heap supporting access to the elements of the heap via handles (also called references). It allows the key of the element referenced by a particular handle to be removed or decreased.

Definition
An addressable heap supports the following operations:


 * , creating an empty heap.
 * , inserting an element  into the heap , and returning a handle to it.
 * , returning a handle to the minimum element, or  if no such element exists.
 * , extracting and returning a handle to the minimum element, or  if no such element exists.
 * , removing the element referenced by  (from its respective heap).
 * , decreasing the key of the element referenced by  to  ; illegal if   is larger than the key referenced by.
 * , combining the elements of  and.

Examples
Examples of addressable heaps include:


 * Fibonacci heaps
 * Binomial heaps

A more complete list with performance comparisons can be found here.