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B-tree

In computer science, 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. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and s. B-trees were invented by Rudolf Bayer and Edward M. McCreight while working at Boeing Research Labs, for the purpose of efficiently managing index pages for large random-access files. The basic assumption was that indices would be so voluminous that only small chunks of the tree could fit in main memory. Bayer and McCreight's paper, Organization and maintenance of large ordered indices, was first circulated in July 1970 and later published in Acta Informatica. Bayer and McCreight never explained what, if anything, the B stands for: Boeing, balanced, between, broad, bushy, and Bayer have been suggested. McCreight has said that "the more you think about what the B in B-trees means, the better you understand B-trees." In 2011 Google developed the C++ B-Tree, reporting a 50-80% reduction in memory use for small data types and improved performance for large data sets when compared to a Red-Black tree. According to Knuth's definition, a B-tree of order m is a tree which satisfies the following properties: Every node has at most m children. Every internal node has at least ⌈m/2⌉ children. The root node has at least two children unless it is a leaf. All leaves appear on the same level. A non-leaf node with k children contains k−1 keys. Each internal node's keys act as separation values which divide its subtrees. For example, if an internal node has 3 child nodes (or subtrees) then it must have 2 keys: a1 and a2. All values in the leftmost subtree will be less than a1, all values in the middle subtree will be between a1 and a2, and all values in the rightmost subtree will be greater than a2.

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