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![Insertion – Step-by-Step Example
• Order = 3 (max 2 keys/node):
• • Insert 10 → [10]
• • Insert 20 → [10, 20]
• • Insert 5 → [5, 10, 20] → Split: [5], [10, 20],
Promote 10
• • Insert 30 → [10, 20, 30] → Split: [10], [20,
30], Promote 20](https://image.slidesharecdn.com/bplustreepresentation-250505191741-bb850d4c/85/BPlus_Tree_Presentation_for_DBMS_Indexing-pptx-7-320.jpg)
BPlus_Tree_Presentation_for_DBMS_Indexing.pptx
- 1. B+ Tree andInsertion in B+ Tree • Database Management Systems (DBMS) • Presented by: Your Name • Institute: Your Institute Name • Date: Presentation Date
- 2. Introduction to B+Tree • • A B+ Tree is a balanced tree used in DBMS and file systems. • • Maintains sorted data with efficient insertion, deletion, and search. • • Stores all data in leaf nodes; internal nodes are for indexing.
- 3. Why Use B+Tree? • • Efficient disk access. • • Supports range queries. • • Balanced structure ensures O(log n) performance. • • Sequential access via linked leaves.
- 4. Structure of B+Tree • • Internal nodes: keys + pointers. • • Leaf nodes: actual data + pointers. • • Linked leaf nodes for fast traversal. • • Uniform depth across all leaves.
- 5. Properties of B+Tree • • Order (m): Max children per node. • • Internal nodes: ≤ m children, ≥ m/2 . ⌈ ⌉ • • Leaf nodes: ≤ m-1 keys, ≥ (m-1)/2 . ⌈ ⌉ • • Root has ≥ 2 children if not leaf.
- 6. Insertion in B+Tree – Overview • 1. Locate the correct leaf node. • 2. Insert key in sorted order. • 3. Handle overflow via split & promote. • 4. Split parent if needed. • 5. Create new root if required.
- 7. Insertion – Step-by-StepExample • Order = 3 (max 2 keys/node): • • Insert 10 → [10] • • Insert 20 → [10, 20] • • Insert 5 → [5, 10, 20] → Split: [5], [10, 20], Promote 10 • • Insert 30 → [10, 20, 30] → Split: [10], [20, 30], Promote 20
- 8. Visualizing Insertion • Includediagrams to illustrate: • - Before and after insertions • - Node splits • - Key promotions
- 9. Advantages of B+Tree • • O(log n) search time. • • Efficient for range queries. • • Balanced and consistent performance. • • Internal nodes guide search only.
- 10. B+ Tree vsB Tree • B Tree: • - Data in internal & leaf nodes • - No linked leaves • B+ Tree: • - Data in leaf nodes only • - Leaves linked for range access
- 11. Applications of B+Tree • • Database indexing • • File systems (e.g., NTFS, ext4) • • Multilevel indexing • • OS file management
- 12. Conclusion • • B+Tree ensures efficient data storage/retrieval. • • Supports quick searches and range queries. • • Key structure for DBMS indexing.
- 13. Q&A • Any questions? •Thank you for your attention!