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Insertion in a B+ Tree

Explore the intricacies of inserting and deleting keys in B+ trees, including handling overflows and underflows. This guide delves into the processes for inserting elements, managing splits, and creating new tree levels, as well as safely deleting keys while maintaining tree balance. Key topics include the effects of insertion at various levels, the challenges of overflow and underflow, and strategies for redistributing or merging nodes. Perfect for students and professionals seeking a deeper understanding of B+ tree algorithms and their implementations.

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Insertion in a B+ Tree

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  1. Insertion in a B+ Tree Insert: 8

  2. 8 Insertion in a B+ Tree Insert: 5

  3. 5 8 Insertion in a B+ Tree Overflow – create a new level Insert: 1

  4. 5 1 5 8 Insertion in a B+ Tree Insert: 7

  5. 5 1 5 7 8 Insertion in a B+ Tree Overflow - Split Insert: 3

  6. 3 5 1 3 5 7 8 Insertion in a B+ Tree Overflow - Split Propagates to a new level Insert: 12

  7. 5 8 3 12 1 3 5 7 8 Insertion in a B+ Tree Insert: 9

  8. 5 8 3 1 3 5 7 8 9 12 Insertion in a B+ Tree Overflow – Split Insert: 6

  9. 5 3 7 8 1 3 5 6 7 8 9 12 Insertion in a B+ Tree Resulting B+-tree

  10. 9 7 1 6 12 1 5 6 7 8 9 Deletion in a B+-Tree Delete: 5

  11. 9 7 1 6 12 1 7 8 9 6 Deletion in a B+-Tree Underflow - redistribute Delete: 12

  12. 8 7 1 6 1 7 6 9 8 Deletion in a B+-Tree Delete: 9

  13. 8 7 1 6 1 7 6 8 Deletion in a B+-Tree Underflow merge with the left propagate reduce the tree levels

  14. 1 6 1 6 7 8 Deletion in a B+-Tree

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