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By A. Bertossi

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For deletion, where a node must be deleted, we scatter to two nodes. The symmetry of the operation allows the gather/scatter routines to be shared by insertion and deletion in the implementation. c. In the implementationdependent section, you’ll need to define bAdrType and eAdrType, the types associated with B-tree file offsets and data file offsets, respectively. You’ll also need to provide a callback function that is used by the B++-tree algorithm to compare keys. Functions are provided to insert/delete keys, find keys, and access keys sequentially.

Duplicates of the keys appear in internal parent nodes to guide the search. Pointers have a slightly different meaning than in conventional B-trees. The left pointer designates all keys less than the value, while the right pointer designates all keys greater than or equal to (GE) the value. For example, all keys less than 22 are on the left pointer, and all keys greater than or equal to 22 are on the right. Notice that key 22 is duplicated in the leaf, where the associated data may be found. During insertion and deletion, care must be taken to properly update parent nodes.

Keys in internal nodes are surrounded by pointers, or record offsets, to keys that are less than or greater than, the key value. For example, all keys less than 22 are to the left and all keys greater than 22 are to the right. For simplicity, I have not shown the record address associated with each key. 22 10 4 6 8 16 12 14 26 18 20 24 28 30 Figure 4-3: B-Tree We can locate any key in this 2-level tree with three disk accesses. If we were to group 100 keys/node, we could search over 1,000,000 keys in only three reads.

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Algoritmi e Strutture di Dati by A. Bertossi

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