**REF.**- Jean Vuillemin. A data structure for manipulating priority queues.
*Communications of the ACM*, Volume 21, Number 4, pp.309-315, 1978. **REF.**- Mark R. Brown. Implementation and analysis of binomial queue algorithms.
*SIAM Journal on Computing*, Volume 7, Number 3, pp. 298-319, 1978.

- Support merge, insert, and deletemin operations in
*O*(log*n*) worstcase time. - A binomial queue is a forest of heap-ordered trees.
- Each of the heap-ordered trees is of a constrained form
known as a
*binomial tree*.

- Each of the heap-ordered trees is of a constrained form
known as a

- A
*binomial tree*of height 0 is a one-node tree; A binomial tree*B*_{k}of height*k*is formed by attaching a binomial tree*B*_{k - 1}to the root of another binomial tree,*B*_{k - 1}. - See Figure 6.5 for an example of binomial tree.
- A binomial tree
*B*_{k}consists of a root with children*B*_{0},*B*_{1}, ...*B*_{k - 1}. *B*_{k}has exactly 2^{k}nodes.- Number of nodes at depth
*d*is*kC*_{d} - If we impose heap order on the binomial trees and allow at most one binomial tree of any height, we can uniquely represent a priority queue of any size by a forest of binomial trees.
**Example**: A priority queue of size 13 could be represented by the forest*B*_{3},*B*_{2},*B*_{0}. A natural way of writing this is: 1101. See Figure 6.6 for a binomial queue with six elements.