Data-intensive Computing Systems Operators for Data Access (contd.) Shivnath Babu 1 Insertion in a B-Tree n=2 49 15 36 49 Insert: 62 2 Insertion in a B-Tree n=2 49 15 36 49 62 Insert: 62 3 Insertion in a B-Tree n=2 49 15 36 49 62 Insert: 50 4 Insertion in a B-Tree 49 15 36 n=2 62 49 50 62 Insert: 50 5 Insertion in a B-Tree 49 15 36 n=2 62 49 50 62 Insert: 75 6 Insertion in a B-Tree 49 15 36 n=2 62 49 50 62 75 Insert: 75 7 Insertion 8 Insertion 9 Insertion 10 Insertion 11 Insertion 12 Insertion 13 Insertion 14 Insertion 15 Insertion 16 Insertion 17 Insertion 18 Insertion: Primitives ◼ Inserting into a leaf node ◼ Splitting a leaf node ◼ Splitting an internal node ◼ Splitting root node 19 Inserting into a Leaf Node 58 54 57 60 62 20 Inserting into a Leaf Node 58 54 57 60 62 21 Inserting into a Leaf Node 58 54 57 58 60 62 22 Splitting a Leaf Node 61 54 54 57 58 60 66 62 23 Splitting a Leaf Node 61 54 54 57 58 60 66 62 24 Splitting a Leaf Node 61 54 54 57 58 66 60 61 62 25 Splitting a Leaf Node 59 61 54 54 57 58 66 60 61 62 26 Splitting a Leaf Node 61 54 54 57 58 59 66 60 61 62 27 Splitting an Internal Node … 21 99 … 59 40 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Splitting an Internal Node … 21 99 … 59 40 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Splitting an Internal Node 66 … 40 54 [54, 59) 21 99 … [21,66) [66, 99) 59 74 [ 59, 66) 84 [66,74) Splitting the Root 59 40 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Splitting the Root 59 40 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Splitting the Root 66 40 54 [54, 59) 59 74 [ 59, 66) 84 [66,74) Deletion 34 Deletion redistribute 35 Deletion 36 Deletion - II 37 Deletion - II merge Deletion - II 39 Deletion - II 40 Deletion - II 41 Deletion - II Not needed merge 42 Del

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