1. CPS216: Advanced Database Systems
Notes 06: Operators for Data Access (contd.)
Shivnath Babu

2. Insertion in a B-Tree
n = 2 49 15 36 49
Insert: 62

3. Insertion in a B-Tree
n = 2 49 15 36 49 62
Insert: 62

4. Insertion in a B-Tree
n = 2 49 15 36 49 62
Insert: 50

5. Insertion in a B-Tree
n = 2 49 62 15 36 49 50 62
Insert: 50

6. Insertion in a B-Tree
n = 2 49 62 15 36 49 50 62
Insert: 75

7. Insertion in a B-Tree
n = 2 49 62 15 36 49 50 62 75
Insert: 75

8. Insertion

9. Insertion

10. Insertion

11. Insertion

12. Insertion

13. Insertion

14. Insertion

15. Insertion

16. Insertion

17. Insertion

18. Insertion

19. Insertion: Primitives
Inserting into a leaf node
Splitting a leaf node
Splitting an internal node
Splitting root node

20. Inserting into a Leaf Node58 54 57 60 62

21. Inserting into a Leaf Node58 54 57 60 62

22. Inserting into a Leaf Node58 54 57 58 60 62

23. Splitting a Leaf Node 61 54 66 54 57 58 60 62

24. Splitting a Leaf Node 61 54 66 54 57 58 60 62

25. Splitting a Leaf Node 61 54 66 54 57 58 60 61 62

26. Splitting a Leaf Node 59 61 54 66 54 57 58 60 61 62

27. Splitting a Leaf Node 61 54 59 66 54 57 58 60 61 62

28. Splitting an Internal Node… 21 99 … 59 40 54 66 74 84
[54, 59)
[ 59, 66)
[66,74)

29. Splitting an Internal Node… 21 99 … 59 40 54 66 74 84
[54, 59)
[ 59, 66)
[66,74)

30. Splitting an Internal Node66 … 21 99 …
[66, 99)
[21,66) 40 54 59 74 84
[54, 59)
[ 59, 66)
[66,74)

31. Splitting the Root 59 40 54 66 74 84
[54, 59)
[ 59, 66)
[66,74)

32. Splitting the Root 59 40 54 66 74 84
[54, 59)
[ 59, 66)
[66,74)

33. Splitting the Root 66 40 54 59 74 84
[54, 59)
[ 59, 66)
[66,74)

34. Deletion

35. Deletion
redistribute

36. Deletion

37. Deletion - II

38. Deletion - II
merge

39. Deletion - II

40. Deletion - II

41. Deletion - II

42. Deletion - II
Not needed
merge

43. Deletion - II

44. Deletion: Primitives Delete key from a leaf
Redistribute keys between sibling leaves
Merge a leaf into its sibling
Redistribute keys between two sibling internal nodes
Merge an internal node into its sibling

45. Merge Leaf into Sibling72 … 67 85 54 58 64 68 72 75

46. Merge Leaf into Sibling72 … 67 85 54 58 64 68 75

47. Merge Leaf into Sibling72 … 67 85 54 58 64 68 75

48. Merge Leaf into Sibling72 … 85 54 58 64 68 75

49. Merge Internal Node into Sibling… 59 … 41 48 52 63 74
[52, 59)
[59,63)

50. Merge Internal Node into Sibling… 59 … 41 48 52 59 63
[52, 59)
[59,63)

51. B-Tree Roadmap B-Tree B-Tree variants Hash-based Indexes Recap
Insertion (recap)
Deletion
Construction
Efficiency
B-Tree variants
Hash-based Indexes

52. How does insertion-based construction perform?
Question
How does insertion-based construction perform?

53. B-Tree Construction
Sort 48 57 41 15 75 21 62 34 81 11 97 13

54. B-Tree Construction 11 13 15 21 34 41 48 57 62 75 81 97 11 13 15 21 34 41 48 57 62 75 81 97
Scan

55. B-Tree Construction 21 48 75 11 13 15 21 34 41 48 57 62 75 81 97
Scan

56. Why is sort-based construction better than insertion-based one?
B-Tree Construction
Why is sort-based construction better than insertion-based one?

57. Cost of B-Tree Operations
Height of B-Tree: H
Assume no duplicates
Question: what is the random I/O cost of:
Insertion:
Deletion:
Equality search:
Range Search:

58. Height of B-Tree Number of keys: N B-Tree parameter: n log N
Height ≈ log N = n
log n
In practice: 2-3 levels

59. Question: How do you pick parameter n?
Ignore inserts and deletes
Optimize for equality searches
Assume no duplicates

60. Roadmap B-Tree B-Tree variants Hash-based Indexes Sparse Index
Duplicate Keys
Hash-based Indexes

61. Roadmap B-Tree B-Tree variants Hash-based Indexes Static Hash Table
Extensible Hash Table
Linear Hash Table

62. Hash-Based Indexes Adaptations of main memory hash tables
Support equality searches
No range searches

63. Indexing Problem (recap)
Index Keys
record pointers a 1 2 i n
A = val

64. Main Memory Hash Table buckets 32 48 (null) 1 key 2 10 (null) h (key)48
(null) 1
key 2 10
(null)
h (key) 3 27 75
(null) 4
h (key) = key % 8 5 21
(null) 6 7 55
(null)

65. Adapting to disk 1 Hash Bucket = 1 Block
All keys that hash to bucket stored in the block
Intuition: keys in a bucket usually accessed together
No need for linked lists of keys …

66. Adapting to Disk
How do we handle this?

67. Adapting to disk 1 Hash Bucket = 1 Block
All keys that hash to bucket stored in the block
Intuition: keys in a bucket usually accessed together
No need for linked lists of keys …
… but need linked list of blocks (overflow blocks)

68. Adapting to Disk

69. Adapting to disk Bucket Id  Disk Address mapping Contiguous blocks
Store mapping in main memory
Too large?
Dynamic  Linear and Extensible hash tables

70. Beware of claims that assume 1 I/O for hash tables and 3 I/Os for B-Tree!!