lec22 - B-Trees Large degree B-trees used to represent very...

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B-Trees Large degree B-trees used to represent very large dictionaries that reside on disk. Smaller degree B-trees used for internal-memory dictionaries to overcome cache-miss penalties.
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AVL Trees
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Red-Black Trees
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m-way Search Trees Each node has up to m – 1 pairs and m children. m = 2 => binary search tree.
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4-Way Search Tree 10 30 35 k < 10 10 < k < 30 30 < k < 35 k > 35
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Maximum # Of Pairs Happens when all internal nodes are m -nodes. Full degree m tree.
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Capacity Of m-Way Search Tree m = 2 m = 200 h = 3 7 8 * 10 6 - 1 h = 5 31 3.2 * 10 11 - 1 h = 7 127 1.28 * 10 16 - 1
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Definition Of B-Tree Definition assumes external nodes (extended m -way search tree). B-tree of order m . m -way search tree. Not empty => root has at least 2 children. Remaining internal nodes (if any) have at least ceil(m/2) children. External (or failure) nodes on same level.
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2-3 And 2-3-4 Trees B-tree of order m . m -way search tree. Not empty => root has at least 2 children.
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