Mergeable Heaps

Union(H1, H2)

Creates and returns a new heap containing all nodes from heaps H1 and H2

Binary Heaps:

Union = $\Theta(n)$ worst case

Binomial Heaps:

Union = $O(\lg n)$ worst case

Fibonacci Heaps:

Union = $\Theta(1)$ amortized

Other operations:

	Binary Heap	Binomial Heap	Fibonacci Heap
	(worst case)	(worst case)	(amortized)
Make-Heap	$\Theta(1)$	$\Theta(1)$	$\Theta(1)$
Minimum	$\Theta(1)$	$\Theta(lgn)$	$\Theta(1)$
Extract-Min	$\Theta(lgn)$	$\Theta(lgn)$	$\Theta(lgn)$
(Union)	$\Theta(n)$	$\Theta(lgn)$	$\Theta(1)$
Decrease-Key	$\Theta(lgn)$	$\Theta(lgn)$	$\Theta(1)$
Delete	$\Theta(lgn)$	$\Theta(lgn)$	$\Theta(lgn)$
Insert	$\Theta(lgn)$	$\Theta(lgn)$	$\Theta(1)$

Extract-Min maintains partial ordering over keys.

This is useful for many graph algorithms.