DBMS Storage and Indexing

1. DBMS Storage and Indexing

2. Disk Storage

3. Disks and Files • DBMS stores information on (“hard”) disks. • This has major implications for DBMS design! • READ: transfer data from disk to main memory (RAM). • WRITE: transfer data from RAM to disk. • Both are high-cost operations, relative to in-memory operations, so must be planned carefully!

4. Why Not Store Everything in Main Memory? • Costs too much. • Main memory is volatile. We want data to be saved between runs. (Obviously!) • Typical storage hierarchy: • Main memory (RAM) for currently used data. • Disk for the main database (secondary storage). • Tapes for archiving older versions of the data (tertiary storage).

5. Disks • Secondary storage device of choice. • Main advantage over tapes: random access vs.sequential. • Data is stored and retrieved in units called disk blocks or pages. • Unlike RAM, time to retrieve a disk page varies depending upon location on disk. • Therefore, relative placement of pages on disk has major impact on DBMS performance!

6. Tracks Arm movement Arm assembly Components of a Disk Spindle Disk head • The platters spin (say, 90rps). • The arm assembly is moved in or out to position a head on a desired track. Tracks under heads make a cylinder(imaginary!). Sector Platters • Only one head reads/writes at any one time. • Block size is a multiple of sector size (which is fixed).

7. Accessing a Disk Page • Time to access (read/write) a disk block: • seek time (moving arms to position disk head on track) • rotational delay (waiting for block to rotate under head) • transfer time (actually moving data to/from disk surface) • Seek time and rotational delay dominate. • Seek time varies from about 1 to 20msec • Rotational delay varies from 0 to 10msec • Transfer rate is about 1msec per 4KB page • Key to lower I/O cost: reduce seek/rotation delays! Hardware vs. software solutions?

8. Arranging Pages on Disk • `Next’ block concept: • blocks on same track, followed by • blocks on same cylinder, followed by • blocks on adjacent cylinder • Blocks in a file should be arranged sequentially on disk (by `next’), to minimize seek and rotational delay. • For a sequential scan, pre-fetchingseveral pages at a time is a big win!

9. RAID • Disk Array: Arrangement of several disks that gives abstraction of a single, large disk. • Goals: Increase performance and reliability. • Two main techniques: • Data striping: Data is partitioned; size of a partition is called the striping unit. Partitions are distributed over several disks. • Redundancy: More disks => more failures. Redundant information allows reconstruction of data if a disk fails.

10. RAID Levels • Level 0: No redundancy • Level 1: Mirrored (two identical copies) • Each disk has a mirror image (check disk) • Parallel reads, a write involves two disks. • Maximum transfer rate = transfer rate of one disk • Level 0+1: Striping and Mirroring • Parallel reads, a write involves two disks. • Maximum transfer rate = aggregate bandwidth

11. RAID Levels (Contd.) • Level 3: Bit-Interleaved Parity • Striping Unit: One bit. One check disk. • Each read and write request involves all disks; disk array can process one request at a time. • Level 4: Block-Interleaved Parity • Striping Unit: One disk block. One check disk. • Parallel reads possible for small requests, large requests can utilize full bandwidth • Writes involve modified block and check disk • Level 5: Block-Interleaved Distributed Parity • Similar to RAID Level 4, but parity blocks are distributed over all disks

12. Disk Space Management • Lowest layer of DBMS software manages space on disk. • Higher levels call upon this layer to: • allocate/de-allocate a page • read/write a page • Request for a sequence of pages must be satisfied by allocating the pages sequentially on disk! Higher levels don’t need to know how this is done, or how free space is managed.

13. DB Buffer Management in a DBMS Page Requests from Higher Levels BUFFER POOL • Data must be in RAM for DBMS to operate on it! • Table of <frame#, pageid> pairs is maintained. disk page free frame MAIN MEMORY DISK choice of frame dictated by replacement policy

14. When a Page is Requested ... • If requested page is not in pool: • Choose a frame for replacement • If frame is dirty, write it to disk • Read requested page into chosen frame • Pin the page and return its address. • If requests can be predicted (e.g., sequential scans) • pages can be pre-fetchedseveral pages at a time!

15. More on Buffer Management • Requestor of page must unpin it, and indicate whether page has been modified: • dirty bit is used for this. • Page in pool may be requested many times, • a pin count is used. A page is a candidate for replacement iff pin count = 0. • CC & recovery may entail additional I/O when a frame is chosen for replacement. (Write-Ahead Log protocol; more later.)

16. Buffer Replacement Policy • Frame is chosen for replacement by a replacement policy: • Least-recently-used (LRU), Clock, MRU etc. • Policy can have big impact on # of I/O’s; depends on the access pattern. • Sequential flooding: Nasty situation caused by LRU + repeated sequential scans. • # buffer frames < # pages in file means each page request causes an I/O. MRU much better in this situation (but not in all situations, of course). • DBMS buffer policy has specific requirements

17. Summary • Disks provide cheap, non-volatile storage. • Random access, but cost depends on location of page on disk; important to arrange data sequentially to minimize seek and rotation delays. • Buffer manager brings pages into RAM. • Page stays in RAM until released by requestor. • Written to disk when frame chosen for replacement (which is sometime after requestor releases the page). • Choice of frame to replace based on replacement policy. • Tries to pre-fetch several pages at a time.

18. Record Organization

19. Record Formats: Fixed Length F1 F2 F3 F4 • Information about field types same for all records in a file; stored in systemcatalogs. • Finding i’th field does not require scan of record. L1 L2 L3 L4 Base address (B) Address = B+L1+L2

20. 4 $ $ $ $ Record Formats: Variable Length F1 F2 F3 F4 • Two alternative formats (# fields is fixed): Fields Delimited by Special Symbols Field Count F1 F2 F3 F4 Array of Field Offsets • Second offers direct access to i’th field, efficient storage • of nulls(special don’t know value); small directory overhead.

21. Page Formats: Fixed Length Records Slot 1 Slot 1 Slot 2 Slot 2 • Record id = <page id, slot #>. In first alternative, moving records for free space management changes rid; may not be acceptable. Free Space . . . . . . Slot N Slot N Slot M N . . . 1 1 1 M 0 M ... 3 2 1 number of records number of slots PACKED UNPACKED, BITMAP

22. Page Formats: Variable Length Records Rid = (i,N) Page i Rid = (i,2) • Can move records on page without changing rid; so, attractive for fixed-length records too. Rid = (i,1) N Pointer to start of free space 20 16 24 N . . . 2 1 # slots SLOT DIRECTORY

23. Files of Records • Page or block is OK when doing I/O, but higher levels of DBMS operate on records, and files of records. • FILE: A collection of pages, each containing a collection of records. Must support: • insert/delete/modify record • read a particular record (specified using record id) • scan all records (possibly with some conditions on the records to be retrieved)

24. File Organization

25. Alternative File Organizations Many alternatives exist, each ideal for some situations, and not so good in others: • Heap (random order) files:Suitable when typical access is a file scan retrieving all records. • Sorted Files: Best if records must be retrieved in some order, or only a `range’ of records is needed. • Indexes: Data structures to organize records via trees or hashing. • Like sorted files, they speed up searches for a subset of records, based on values in certain (“search key”) fields • Updates are much faster than in sorted files.

26. Unordered (Heap) Files • Simplest file structure contains records in no particular order. • As file grows and shrinks, disk pages are allocated and de-allocated. • To support record level operations, we must: • keep track of the pages in a file • keep track of free space on pages • keep track of the records on a page • There are many alternatives for keeping track of this.

27. Heap File Implemented as a List Data Page Data Page Data Page • The header page id and Heap file name must be stored someplace. • Each page contains 2 `pointers’ plus data. Full Pages Header Page Data Page Data Page Data Page Pages with Free Space

28. Data Page 1 Header Page Data Page 2 Data Page N DIRECTORY Heap File Using a Page Directory • The entry for a page can include the number of free bytes on the page. • The directory is a collection of pages; linked list implementation is just one alternative. • Much smaller than linked list of all HF pages!

29. System Catalogs • For each index: • structure (e.g., B+ tree) and search key fields • For each relation: • name, file name, file structure (e.g., Heap file) • attribute name and type, for each attribute • index name, for each index • integrity constraints • For each view: • view name and definition • Plus statistics, authorization, buffer pool size, etc. • Catalogs are themselves stored as relations!

30. Index Structures

31. Indexes • An index on a file speeds up selections on the search key fields for the index. • Any subset of the fields of a relation can be the search key for an index on the relation. • Search key is not the same as key (minimal set of fields that uniquely identify a record in a relation). • An index contains a collection of data entries, and supports efficient retrieval of all data entries k*with a given key value k. • Given data entry k*, we can find record with key k in at most one disk I/O. (Details soon …)

32. Alternatives for Data Entry k*in Index • In a data entry k* we can store: • Data record with key value k, or • <k, rid of data record with search key value k>, or • <k, list of rids of data records with search key k> • Choice of alternative for data entries is orthogonal to the indexing technique used to locate data entries with a given key value k. • Examples of indexing techniques: B+ trees, hash-based structures • Typically, index contains auxiliary information that directs searches to the desired data entries

33. Alternatives for Data Entries (Contd.) • Alternative 1: • If this is used, index structure is a file organization for data records (instead of a Heap file or sorted file). • At most one index on a given collection of data records can use Alternative 1. (Otherwise, data records are duplicated, leading to redundant storage and potential inconsistency.) • If data records are very large, # of pages containing data entries is high. Implies size of auxiliary information in the index is also large, typically.

34. Alternatives for Data Entries (Contd.) • Alternatives 2 and 3: • Data entries typically much smaller than data records. So, better than Alternative 1 with large data records, especially if search keys are small. (Portion of index structure used to direct search, which depends on size of data entries, is much smaller than with Alternative 1.) • Alternative 3 more compact than Alternative 2, but leads to variable sized data entries even if search keys are of fixed length.

35. Index Classification • Primary vs. secondary: If search key contains primary key, then called primary index. • Unique index: Search key contains a candidate key. • Clustered vs. unclustered: If order of data records is the same as, or `close to’, order of data entries, then called clustered index. • Alternative 1 implies clustered; in practice, clustered also implies Alternative 1 (since sorted files are rare). • A file can be clustered on at most one search key. • Cost of retrieving data records through index varies greatly based on whether index is clustered or not!

36. Clustered vs. Unclustered Index • Suppose that Alternative (2) is used for data entries, and that the data records are stored in a Heap file. • To build clustered index, first sort the Heap file (with some free space on each page for future inserts). • Overflow pages may be needed for inserts. (Thus, order of data recs is `close to’, but not identical to, the sort order.) Index entries UNCLUSTERED CLUSTERED direct search for data entries Data entries Data entries (Index File) (Data file) Data Records Data Records

37. Tree-Structured Indexes

38. Introduction • As for any index, 3 alternatives for data entries k*: • Data record with key value k • <k, rid of data record with search key value k> • <k, list of rids of data records with search key k> • Choice is orthogonal to the indexing technique used to locate data entries k*. • Tree-structured indexing techniques support both range searches and equality searches. • ISAM: static structure;B+ tree: dynamic, adjusts gracefully under inserts and deletes.

39. Range Searches • ``Find all students with gpa > 3.0’’ • If data is in sorted file, do binary search to find first such student, then scan to find others. • Cost of binary search can be quite high. • Simple idea: Create an `index’ file. Index File kN k2 k1 Data File Page N Page 3 Page 1 Page 2 • Can do binary search on (smaller) index file!

40. Index Entries (Direct search) Data Entries ("Sequence set") B+ Tree: Most Widely Used Index • Insert/delete at log F N cost; keep tree height-balanced. (F = fanout, N = # leaf pages) • Minimum 50% occupancy (except for root). Each node contains d <= m <= 2d entries. The parameter d is called the order of the tree. • Supports equality and range-searches efficiently.

41. Example B+ Tree • Search begins at root, and key comparisons direct it to a leaf. • Search for 5*, 15*, all data entries >= 24* ... Root 30 13 17 24 39* 3* 5* 19* 20* 22* 24* 27* 38* 2* 7* 14* 16* 29* 33* 34* • Based on the search for 15*, we know it is not in the tree!

42. B+ Trees in Practice • Typical order: 100. Typical fill-factor: 67%. • average fanout = 133 • Typical capacities: • Height 4: 1334 = 312,900,700 records • Height 3: 1333 = 2,352,637 records • Can often hold top levels in buffer pool: • Level 1 = 1 page = 8 Kbytes • Level 2 = 133 pages = 1 Mbyte • Level 3 = 17,689 pages = 133 MBytes

43. 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 splitL (into L and a new node L2) • Redistribute entries evenly, copy upmiddle key. • Insert index entry pointing to L2 into parent of L. • This can happen recursively • To split index node, redistribute entries evenly, but push upmiddle key. (Contrast with leaf splits.) • Splits “grow” tree; root split increases height. • Tree growth: gets wider or one level taller at top.

44. Entry to be inserted in parent node. (Note that 17 is pushed up and only 17 this with a leaf split.) 5 13 24 30 Inserting 8* into Example B+ Tree Entry to be inserted in parent node. • Observe how minimum occupancy is guaranteed in both leaf and index pg splits. • Note difference between copy-upand push-up; be sure you understand the reasons for this. (Note that 5 is s copied up and 5 continues to appear in the leaf.) 3* 5* 2* 7* 8* appears once in the index. Contrast

45. Example B+ Tree After Inserting 8* Root 17 24 5 13 30 39* 2* 3* 5* 7* 8* 19* 20* 22* 24* 27* 38* 29* 33* 34* 14* 16* • Notice that root was split, leading to increase in height. • In this example, we can avoid split by re-distributing entries; however, this is usually not done in practice.

46. 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, mergeL and sibling. • If merge occurred, must delete entry (pointing to L or sibling) from parent of L. • Merge could propagate to root, decreasing height.

47. Example Tree After (Inserting 8*, Then) Deleting 19* and 20* ... Root • Deleting 19* is easy. • Deleting 20* is done with re-distribution. Notice how middle key is copied up. 17 27 5 13 30 39* 2* 3* 5* 7* 8* 22* 24* 27* 29* 38* 33* 34* 14* 16*

48. ... And Then Deleting 24* 30 • Must merge. • Observe `toss’ of index entry (on right), and `pull down’ of index entry (below). 39* 22* 27* 38* 29* 33* 34* Root 5 13 17 30 3* 39* 2* 5* 7* 8* 22* 38* 27* 33* 34* 14* 16* 29*

49. 2* 3* 5* 7* 8* 39* 17* 18* 38* 20* 21* 22* 27* 29* 33* 34* 14* 16* 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 30 17 20 5 13

50. After Re-distribution • Intuitively, entries are re-distributed by `pushingthrough’ 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 22 30 5 13 20 2* 3* 5* 7* 8* 39* 17* 18* 38* 20* 21* 22* 27* 29* 33* 34* 14* 16*