B Trees

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B Trees

  1. 1. B Trees
  2. 2. Sample B tree
  3. 3. <ul><li>Minimization Factor : No of allowable Children for each node </li></ul><ul><li>every node must have at least t - 1 keys </li></ul><ul><li>Every node may have at most 2t - 1 </li></ul>
  4. 4. <ul><li>the height of an n -key b-tree </li></ul><ul><li>With t greater than or equal to 2, </li></ul>
  5. 5. Sample B tree
  6. 7. B-tree of order 5 all internal nodes have at least ceil(5 / 2) = ceil(2.5) = 3 children maximum number of children that a node can have is 5
  7. 8. Insertion <ul><li>B-tree of order 5: </li></ul><ul><li>C N G A H E K Q M F W L T Z D P R X Y S </li></ul><ul><li>Order 5 means that a node can have a maximum of 5 children and 4 keys. </li></ul><ul><li>All nodes other than the root must have a minimum of 2 keys. </li></ul>
  8. 9. <ul><li>C N G A Order this ACGN </li></ul><ul><li>Inserting ACGN </li></ul>
  9. 10. Inserting H
  10. 11. Inserting E, K, and Q proceeds without requiring any splits:
  11. 12. Inserting M requires a split
  12. 13. The letters F, W, L, and T are then added without needing any split
  13. 14. Adding Z
  14. 15. Inserting D
  15. 16. Inserting s
  16. 17. DELETION (H)
  17. 18. Delete T
  18. 19. Delete R
  19. 20. Delete E

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