lec24 - B-Trees Same structure as B-trees Dictionary pairs...

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B + -Trees Same structure as B-trees. Dictionary pairs are in leaves only. Leaves form a doubly-linked list. Remaining nodes have following structure: j = number of keys in node.
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Example B+-tree 9 5 1 3 5 6 30 40 9 16 17 16 30 index node leaf/data node
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B+-tree—Search 9 5 1 3 5 6 30 40 9 16 17 16 30 key = 5 6 <= key <= 20
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B+-tree—Insert 9 5 5 6 30 40 9 16 17 16 30 Insert 10 1
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16 30 Insert 9 5 1 3 5 6 30 40 9 Insert a pair with key = 2 . New pair goes into a 3 -node. 16 17
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Insert Into A 3-node Insert new pair so that the keys are in ascending order. Split into two nodes. 2 3 1 1 2 3 Insert smallest key in new node and pointer to this new node into parent. 2 2 3 1
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9 Insert 9 5 5 6 30 40 16 17 2 Insert an index entry 2 plus a pointer into parent. 2 3 1 16 30
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Insert Now, insert a pair with key = 18 . 9 1 2 5 5 6 30 40 9 16 17 16 30 2 3
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Insert Now, insert a pair with key = 18 . 9 1 2 5 5 6 30 40 9 16 30 2 3 16 17 17 18 Insert an index entry 17 plus a pointer into parent.
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Insert Now, insert a pair with key = 18 .
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