Mergeable Heap Operations

Make-Heap, Insert, Minimum, Extract-Min, Union

These always yield unordered binomial trees; thus, they maintain the binomial tree properties.

1.

2^k nodes

2.

k = height of tree

3.

nodes at depth i

4.

Unordered binomial tree U_k has root with degree k greater than any other node. Children are trees U₀, U₁, .., U_k-1 in some order.

For n-node Fibonacci Heap, D(n) is largest if all nodes are in one tree.

The maximum degree is at depth=1, = k for tree with 2^k nodes.

If n = 2^k, then k = lg n

D(n) $\leq$ k = lg n

D(n) = O(lg n)