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.

• Magic Circles
• Magic Constant
• Magic Cube
• Magic Geometric Constants
• Magic Graph
• Magic Hexagon
• Magic Labeling
• Magic Number
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• Magic Tour
• Mahler-Lech Theorem
• Mahler's Measure
• Mainardi-Codazzi Equations
• Majorant
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• Makeham Curve
• Malfatti Circles
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• Malfatti's Right Triangle Problem
• Malfatti's Tangent Triangle Problem
• Malliavin Calculus
• Mallow's Sequence