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use the B+ -tree structure not only as an index, but also as an organizer for records in a le In a B+ -tree le organization, the leaf nodes of the tree store records, instead of storing pointers to records Figure 1218 shows an example of a B+ -tree le organization Since records are usually larger than pointers, the maximum number of records that can be stored in a leaf node is less than the number of pointers in a nonleaf node However, the leaf nodes are still required to be at least half full Insertion and deletion of records from a B+ -tree le organization are handled in the same way as insertion and deletion of entries in a B+ -tree index When a record with a given key value v is inserted, the system locates the block that should contain the record by searching the B+ -tree for the largest key in the tree that is v If the block located has enough free space for the record, the system stores the record in the block Otherwise, as in B+ -tree insertion, the system splits the block in two, and redistributes the records in it (in the B+ -tree key order) to create space for the new record The split propagates up the B+ -tree in the normal fashion When we delete a record, the system rst removes it from the block containing it If a block B becomes less than half full as a result, the records in B are redistributed with the records in an adjacent block B Assuming xed-sized records, each block will hold at least one-half as many records as the maximum that it can hold The system updates the nonleaf nodes of the B+ -tree in the usual fashion When we use a B+ -tree for le organization, space utilization is particularly important, since the space occupied by the records is likely to be much more than the space occupied by keys and pointers We can improve the utilization of space in a B+ tree by involving more sibling nodes in redistribution during splits and merges The technique is applicable to both leaf nodes and internal nodes, and works as follows During insertion, if a node is full the system attempts to redistribute some of its entries to one of the adjacent nodes, to make space for a new entry If this attempt fails because the adjacent nodes are themselves full, the system splits the node, and splits the entries evenly among one of the adjacent nodes and the two nodes that it obtained by splitting the original node Since the three nodes together contain one more record than can t in two nodes, each node will be about two-thirds full More precisely, each node will have at least 2n/3 entries, where n is the maximum number of entries that the node can hold ( x denotes the greatest integer that is less than or equal to x; that is, we drop the fractional part, if any)
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Silberschatz Korth Sudarshan: Database System Concepts, Fourth Edition
IV Data Storage and Querying
12 Indexing and Hashing
The McGraw Hill Companies, 2001
12
Indexing and Hashing
During deletion of a record, if the occupancy of a node falls below 2n/3 , the system attempts to borrow an entry from one of the sibling nodes If both sibling nodes have 2n/3 records, instead of borrowing an entry, the system redistributes the entries in the node and in the two siblings evenly between two of the nodes, and deletes the third node We can use this approach because the total number of entries is 3 2n/3 1, which is less than 2n With three adjacent nodes used for redistribution, each node can be guaranteed to have 3n/4 entries In general, if m nodes (m 1 siblings) are involved in redistribution, each node can be guaranteed to contain at least (m 1)n/m entries However, the cost of update becomes higher as more sibling nodes are involved in the redistribution
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