Define a binomial heap and its characteristics.

A binomial heap is a specific type of data structure that is a collection of binomial trees.

A binomial heap is a type of heap similar to a binary heap but also supports quick merging of two heaps. This is achieved by using a special tree structure, where each binomial heap is a set of binomial trees. Each of these trees follows the min-heap property, meaning the parent node is always smaller than or equal to its child nodes.

A binomial tree of order 0 has 1 node. A binomial tree of order k can be constructed by taking two binomial trees of order k-1 and making one as leftmost child or sibling of the other. This property makes the binomial heap efficient and easy to manage, as trees of different orders can be linked together to form a new heap.

The binomial heap has several key characteristics. Firstly, it supports several operations including insertion, deletion and extraction of the minimum element, each with a logarithmic running time. Secondly, it allows the merging of two binomial heaps in a time complexity of O(log n), which is more efficient than other types of heaps.

Another important characteristic of a binomial heap is that it is a collection of binomial trees that are arranged in increasing order of their degrees. This means that for a binomial heap with n nodes, the number of trees is at most log(n) + 1. This property ensures that the height of the heap remains relatively small, even as the number of elements increases, which contributes to its efficiency.

In summary, a binomial heap is a powerful data structure that combines the advantages of a binary heap with the ability to merge heaps quickly. Its structure of binomial trees ensures that operations can be performed efficiently, making it a useful tool in many areas of computer science.