ch9-btrees - 2001-2009 M D Evans All Rights Reserved 1 Ch 9...

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Unformatted text preview: 2001-2009 M. D. Evans All Rights Reserved 1 Ch 9. B–Trees: (after R. Bayer) 9.1 Introduction: Question : If 2–3 tree good vs BBST, are trees with nodes having > 3 children better? Points to consider: more values/node ==> 1. Reduced tree height ⇒ fast log search. 2. Longer sequential searches within node (but ordered data ⇒ binary search ok) 2001-2009 M. D. Evans All Rights Reserved 2 Def: B–tree of order m is an m-way search tree: - All leaves are on the same level. - All internal nodes (except root) have at most m (non- empty) children and at least [m/2] (non-empty) children. - The # of keys in an internal node is 1 less than # of its children. - The # of keys in a leaf node is between (m/2 – 1) and (m- 1) children. - Keys in a node are arranged in some search order. - The root has at most m children, and at least 2 children (unless it is a leaf). Note : a 2-3 tree is a B-tree of order 3. 2001-2009 M. D. Evans All Rights Reserved 3 Example: B-tree of order 5 ....
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This note was uploaded on 05/13/2010 for the course CMPT 225 taught by Professor Annelavergne during the Spring '07 term at Simon Fraser.

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ch9-btrees - 2001-2009 M D Evans All Rights Reserved 1 Ch 9...

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