B-Tree

-trees were introduced by Bayer (1972) and McCreight. They are a special -ary balanced tree used in databases becausetheir structure allows records to be inserted, deleted, and retrieved with guaranteed worst-case performance. An -node-tree has height , where Lg is the Logarithm to base 2. The AppleMacintosh (Apple Computer, Cupertino, CA) HFS filing system uses -trees to store disk directories(Benedict 1995). A -tree satisfies the following properties:

1. The Root is either a Leaf (Tree) or has at least two Children.

2. Each node (except the Root and Leaves) has between and Children, where is the Ceiling Function.

3. Each path from the Root to a Leaf (Tree) has the same length.

Every 2-3 Tree is a -tree of order 3. The number of -trees of order 3 with , 2, ... leaves are 1, 1, 1, 1, 2, 2, 3, 4, 5, 8, 14, 23, 32, 43, 63, ... (Ruskey, Sloane's A014535).

References

Aho, A. V.; Hopcroft, J. E.; and Ullmann, J. D. Data Structures and Algorithms. Reading, MA: Addison-Wesley, pp. 369-374, 1987.

Benedict, B. Using Norton Utilities for the Macintosh. Indianapolis, IN: Que, pp. B-17-B-33, 1995.

Beyer, R. ``Symmetric Binary -Trees: Data Structures and Maintenance Algorithms.'' Acta Informat. 1, 290-306, 1972.

Ruskey, F. ``Information on B-Trees.'' http://sue.csc.uvic.ca/~cos/inf/tree/BTrees.html.

Sloane, N. J. A. Sequence A014535in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

• Iff
• Ill-Conditioned
• Illumination Problem
• Illusion
• Image
• Imaginary Identity
• Imaginary Number
• Imaginary Part
• Imaginary Point
• Imaginary Quadratic Field
• Immanant
• Immersed Minimal Surface
• Immersion
• Impartial Game
• Implicit Function
• Implicit Function Theorem
• Implies
• Impossible Figure
• Impredicative
• Improper Integral
• Improper Node
• Improper Rotation
• Impulse Pair
• Impulse Symbol
• Inaccessible Cardinal