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Indexing (cont.)

Indexing (cont.). Insertion in a B+ Tree. Another B+ Tree. 10. 15. 18. 19. 20. 25. 30. 40. 50. 60. 65. 80. 85. 90. Insertion in a B+ Tree. Now Insert 12. 10. 15. 18. 19. 20. 25. 30. 40. 50. 60. 65. 80. 85. 90. Insertion in a B+ Tree. Need to split leaf. 10. 12.

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Indexing (cont.)

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  1. Indexing (cont.)

  2. Insertion in a B+ Tree Another B+ Tree 10 15 18 19 20 25 30 40 50 60 65 80 85 90

  3. Insertion in a B+ Tree Now Insert 12 10 15 18 19 20 25 30 40 50 60 65 80 85 90

  4. Insertion in a B+ Tree Need to split leaf 10 12 15 18 19 20 25 30 40 50

  5. Insertion in a B+ Tree Need to split branch 10 12 15 18 19 20 25 30 40 50

  6. Insertion in a B+ Tree After split 10 12 15 18 19 20 25 30 40 50

  7. Deleting a Data Entry from a B+ Tree • Start at root, find leaf L where entry belongs. • Remove the entry. • If L is at least half-full, done! • If L has only d-1 entries, • Try to re-distribute, borrowing from sibling (adjacent node with same parent as L). • If re-distribution fails, mergeL and sibling. • If merge occurred, must delete entry (pointing to L or sibling) from parent of L. • Merge could propagate to root, decreasing height.

  8. Deletion from a B+ Tree Delete 30 10 15 18 19 20 25 30 40 50 60 65 80 85 90

  9. Deletion from a B+ Tree After deleting 30 May change to 40, or not 10 15 18 19 20 25 40 50 60 65 80 85 90

  10. Deletion from a B+ Tree Now delete 25 10 15 18 19 20 25 40 50 60 65 80 85 90

  11. Deletion from a B+ Tree After deleting 25 Need to rebalance Rotate 10 15 18 19 20 40 50 60 65 80 85 90

  12. Deletion from a B+ Tree Now delete 40 10 15 18 19 20 40 50 60 65 80 85 90

  13. Deletion from a B+ Tree After deleting 40 Rotation not possible Need to merge nodes 10 15 18 19 20 50 60 65 80 85 90

  14. Deletion from a B+ Tree Final tree 10 15 18 19 20 50 60 65 80 85 90

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