A B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. It is a generalization of the binary search tree in that a B-tree allows for nodes to have more than two children, making it a multi-way tree[1][2].
Characteristics of B-Trees
Balanced Tree: B-trees are balanced, meaning that all leaf nodes are at the same level. This balance ensures that operations such as search, insert, and delete all have a time complexity of $$O(\log n)$$, where $$n$$ is the number of elements in the tree[1][2][3][10].
Nodes with Multiple Keys: Each node in a B-tree can hold multiple keys and have multiple children. The number of keys is one less than the number of children. The keys act as separation values which divide the tree into sub-trees[1][2].
Order of the Tree: The order of a B-tree is a measure of its capacity. It defines the maximum number of children a node can have. For a B-tree of order $$m$$, each internal node can have at most $$m$$ children and at least $$\lceil m/2 \rceil$$ children, except for the root[1][2][6].
Efficient Disk Access: B-trees are particularly well-suited for storage systems that deal with large blocks of data, such as databases and file systems. This is because B-trees minimize the number of disk accesses required to find a particular element, thereby speeding up operations[1][2][11].
Operations on B-Trees
Search: To find a key in a B-tree, start at the root and traverse the tree by making decisions at each node based on the key values stored in the nodes. This operation takes $$O(\log n)$$ time[1][2].
