Lecture6 - ECS 165B: Database System Implementa6on Lecture...

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Unformatted text preview: ECS 165B: Database System Implementa6on Lecture 6 UC Davis April 9, 2010 Acknowledgements: por6ons based on slides by Raghu Ramakrishnan and Johannes Gehrke. Class Agenda Last 6me: Record Manager cookbook session Today: An announcement! Dynamic aspects of B+ Trees Reading Chapter 10 in Ramakrishan and Gehrke (or Chapter 12 in Silberschatz, Korth, and Sudarshan) Announcements EXTENSION: Project Part 1 deadline pushed back 1 week now due Sunday 4/18 @11:59pm TO ACCOMMODATE EXTENSION: Deadlines for Parts 2-4 also pushed back 1 week Project Part 5 cancelled Dynamic Aspects of B+ Trees Example B+ Tree Search begins at root, and key comparisons direct it to a leaf (as in ISAM). Search for 5*, 15*, all data entries >= 24* ... Root 13 17 24 30 2* 3* 5* 7* 14* 16* 19* 20* 22* 24* 27* 29* 33* 34* 38* 39* * Based on the search for 15*, we know it is not in the tree! Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 10 Inserting a Data Entry into a B+ Tree Find correct leaf L. Put data entry onto L. If L has enough space, done! Else, must split L (into L and a new node L2) Redistribute entries evenly, copy up middle key. Insert index entry pointing to L2 into parent of L. This can happen recursively To split index node, redistribute entries evenly, but push up middle key. (Contrast with leaf splits.) Splits "grow" tree; root split increases height. Tree growth: gets wider or one level taller at top. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 12 Example Example B+ Tree B+ Tree Search begins at root, and key comparisons direct it to a leaf (as in ISAM). Search for 5*, 15*, all data entries >= 24* ... Root 13 17 24 30 2* 3* 5* 7* 14* 16* 19* 20* 22* 24* 27* 29* 33* 34* 38* 39* * Based on the search for 15*, we know it is not in the tree! Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 10 Inserting 8* into Example B+ Tree Observe how minimum occupancy is guaranteed in both leaf and index pg splits. Note difference between copyup and push-up; be sure you understand the reasons for this. 5 Entry to be inserted in parent node. (Note that 5 is copied up and s continues to appear in the leaf.) 2* 3* 5* 7* 8* 17 Entry to be inserted in parent node. (Note that 17 is pushed up and only appears once in the index. Contrast this with a leaf split.) 5 13 24 30 Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 13 Search begins at root, and key comparisons direct it to a leaf (as in ISAM). Inser6ng 5*, 15*, all xample B+ >= 24* ... 8* Into Edata entries Tree Search for Root Inserting 8* into Example B+ T ing 8* into Example B+ Tree w s in d its. nce Observe how 17 24 30 13 5 minimum occupancy is 5* 7* 8* 2* 3* 19* 24* 27* 29* 2* 3* 5* 7* guaranteed in 20* 22* 14* 16* 33* 34* 38* 39* both leaf and * Based on the pg splits. we know it is not in the tree! index search for 15*, Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 10 Note difference Entry to be insert (Note that 17 is Entry to between copy- be inserted in parent node. 17 appears once in the pu in (Note that 5 is copied up and this with a leaf sp s 5 up and push-up; to appear in the leaf.) continues be sure you 5 13 24 30 understand the 5* 7* 8* 2* 3* reasons for this. Entry to be insert (Note that 5 is co s continues to app B+ Trees in Practice Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke Example B+ Tree After Inserting 8* Root 17 5 13 24 30 2* 3* 5* 7* 8* 14* 16* 19* 20* 22* 24* 27* 29* 33* 34* 38* 39* v Notice that root was split, leading to increase in height. v In this example, we can avoid split by re-distributing entries; however, this is usually not done in practice. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 14 Deleting a Data Entry from a B+ Tree Start at root, find leaf L where entry belongs. Remove the entry. If L is at least half-full, done! If L has only d-1 entries, Try to re-distribute, borrowing from sibling (adjacent node with same parent as L). If re-distribution fails, merge L and sibling. If merge occurred, must delete entry (pointing to L or sibling) from parent of L. Merge could propagate to root, decreasing height. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 15 Example Tree After (Inserting 8*, Then) Deleting 19* and 20* ... Root 17 5 13 27 30 2* 3* 5* 7* 8* 14* 16* 22* 24* 27* 29* 33* 34* 38* 39* Deleting 19* is easy. Deleting 20* is done with re-distribution. Notice how middle key is copied up. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 16 Example B+ Tree After Inserting 20* Example Tree Before/A_er Dele6ng 19* and 8* Root Before: 5 13 17 2* 3* Example Tree After (Inserting 8*, Then) Deleting 19* and 20* ... 24 30 5* 7* 8* 14* 16* 19* 20* 22* 24* 27* 29* 33* 34* 38* 39* Root A_er: 17 v Notice that root was split, leading to increase in height. v In this example, we can avoid split by 27 30 re-distributing 5 13 entries; however, this is usually not done in practice. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 2* 3* 5* 7* 8* 14* 16* 22* 24* 27* 29* 33* 34* 38* 39* 14 Deleting 19* is easy. ... And Then Deleting 24* Must merge. Observe `toss' of index entry (on right), and `pull down' of index entry (below). Root 5 13 17 30 30 22* 27* 29* 33* 34* 38* 39* 2* 3* 5* 7* 8* 14* 16* 22* 27* 29* 33* 34* 38* 39* Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 17 Example of Non-leaf Re-distribution Tree is shown below during deletion of 24*. (What could be a possible initial tree?) In contrast to previous example, can re-distribute entry from left child of root to right child. Root 22 5 13 17 20 30 2* 3* 5* 7* 8* 14* 16* 17* 18* 20* 21* 22* 27* 29* 33* 34* 38* 39* Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 18 Example Tree After (Inserting 8*, Then)Before/A_er Dele6ng 24* ... Deleting 19* and 20* ... And Then Deleting 24* Root 17 Before: Must 5merge. 13 Observe `toss' of 2* index entry (on right), 3* 5* 7* 8* 14* 16* and `pull down' of index entry 19* is easy. Deleting (below). 27 30 30 22* 24* 27* 29* 33* 34* 38* 39* 22* 27* 29* 33* 34* 38* 39* During: Deleting 20* is done with re-distribution. Root Notice how middle key is copied up. 5 13 17 30 16 Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 2* 3* 5* 7* 8* 14* 16* 22* 27* 29* 33* 34* 38* 39* Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 17 After Re-distribution Intuitively, entries are re-distributed by `pushing through' the splitting entry in the parent node. It suffices to re-distribute index entry with key 20; we've re-distributed 17 as well for illustration. Root 17 5 13 20 22 30 2* 3* 5* 7* 8* 14* 16* 17* 18* 20* 21* 22* 27* 29* 33* 34* 38* 39* Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 19 B+ Tree Dele6on in DavisDB Standard dele6on algorithm is tricky to implement (many corner cases) We'll use a simplified version of scheme: lazy dele(on When entry is deleted, no redistribu6on or node merge even if leaf page < half full; underfull page remains in tree Prefix Key Compression Important to increase fan-out. (Why?) Key values in index entries only `direct traffic'; can often compress them. E.g., If we have adjacent index entries with search key values Dannon Yogurt, David Smith and Devarakonda Murthy, we can abbreviate David Smith to Dav. (The other keys can be compressed too ...) Is this correct? Not quite! What if there is a data entry Davey Jones? (Can only compress David Smith to Davi) In general, while compressing, must leave each index entry greater than every key value (in any subtree) to its left. Insert/delete must be suitably modified. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 20 Bulk Loading of a B+ Tree If we have a large collection of records, and we want to create a B+ tree on some field, doing so by repeatedly inserting records is very slow. Bulk Loading can be done much more efficiently. Initialization: Sort all data entries, insert pointer to first (leaf) page in a new (root) page. Root Sorted pages of data entries; not yet in B+ tree 3* 4* 6* 9* 10* 11* 12* 13* 20* 22* 23* 31* 35* 36* 38* 41* 44* Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 21 Bulk Loading (Contd.) Root 10 20 Index entries for leaf pages always entered into rightmost index page just 3* above leaf level. When this fills up, it splits. (Split may go up right-most path to the root.) Much faster than repeated inserts, especially when one considers locking! 6 12 23 35 Data entry pages not yet in B+ tree 4* 6* 9* 10* 11* 12* 13* 20*22* 23* 31* 35* 36* 38* 41* 44* Root 20 10 35 Data entry pages not yet in B+ tree 38 6 12 23 Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 3* 4* 6* 9* 10* 11* 12* 13* 20*22* 23* 31* 35* 36* 38* 41* 44* 22 Summary of Bulk Loading Option 1: multiple inserts. Slow. Does not give sequential storage of leaves. Option 2: Bulk Loading Has advantages for concurrency control. Fewer I/Os during build. Leaves will be stored sequentially (and linked, of course). Can control "fill factor" on pages. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 23 A Note on `Order' Order (d) concept replaced by physical space criterion in practice (`at least half-full'). Index pages can typically hold many more entries than leaf pages. Variable sized records and search keys mean differnt nodes will contain different numbers of entries. Even with fixed length fields, multiple records with the same search key value (duplicates) can lead to variable-sized data entries (if we use Alternative (3)). Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 24 Duplicate Keys Several data entries may have same key value; what if, e.g., there are too many to fit on a single leaf page? Solu6on 1 (rare): Use overflow leaf pages, as in ISAM Solu6on 2 (common): Use spligng as usual, allowing duplicate key values in index nodes Range search: find le/most data entry with given key value; scan When record is deleted, have to scan all records with that key value (can be slow) Solu6on 3: expand key to include record id (rules out duplicates) Fast dele6on; but index takes more space Summary Tree-structured indexes are ideal for rangesearches, also good for equality searches. ISAM is a static structure. Only leaf pages modified; overflow pages needed. Overflow chains can degrade performance unless size of data set and data distribution stay constant. B+ tree is a dynamic structure. Inserts/deletes leave tree height-balanced; log F N cost. High fanout (F) means depth rarely more than 3 or 4. Almost always better than maintaining a sorted file. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 25 Summary (Contd.) Typically, 67% occupancy on average. Usually preferable to ISAM, modulo locking considerations; adjusts to growth gracefully. If data entries are data records, splits can change rids! Key compression increases fanout, reduces height. Bulk loading can be much faster than repeated inserts for creating a B+ tree on a large data set. Most widely used index in database management systems because of its versatility. One of the most optimized components of a DBMS. Database Management Systems 3ed, R. Ramakrishnan and J. Gehrke 26 ...
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