Mergeable heap

In computer science, a mergeable heap (also called a meldable heap) is an abstract data type, which is a heap supporting a merge operation.

Definition

A mergeable heap supports the usual heap operations: Make-Heap(), create an empty heap. Insert(H,x), insert an element x into the heap H. Min(H), return the minimum element, or Nil if no such element exists. Extract-Min(H), extract and return the minimum element, or Nil if no such element exists.

And one more that distinguishes it: Merge(H1,H2), combine the elements of H1 and H2 into a single heap.

Trivial implementation

It is straightforward to implement a mergeable heap given a simple heap:

Merge(H1,H2): x ← Extract-Min(H2) while x ≠ Nil Insert(H1, x) x ← Extract-Min(H2)

This can however be wasteful as each Extract-Min(H) and Insert(H,x) typically have to maintain the heap property.

More efficient implementations

Examples of mergeable heap data structures include:

Binomial heap Fibonacci heap Leftist tree Pairing heap Skew heap

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

In most mergeable heap structures, merging is the fundamental operation on which others are based. Insertion is implemented by merging a new single-element heap with the existing heap. Deletion is implemented by merging the children of the deleted node.

See also Addressable heap

References