Transcript database_index_tutorial

DBMS Storage and Indexing
Disk Storage
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!
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).
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!
Components of a Disk
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
Arm movement
Only one head
reads/writes at any one time.

Block size is a multiple
(which is fixed).

Spindle
Tracks
Arm assembly
of sector size
Platters
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?
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-fetching several
pages at a time is a big win!
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.
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
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
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.
Buffer Management in a DBMS
Page Requests from Higher Levels
BUFFER POOL
disk page
free frame
MAIN MEMORY
DISK
DB
choice of frame dictated
by replacement policy
• Data must be in RAM for DBMS to operate on it!
• Table of <frame#, pageid> pairs is maintained.
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-fetched several pages at a time!
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.)
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
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.
Record Organization
Record Formats: Fixed Length
F1
F2
F3
F4
L1
L2
L3
L4
Base address (B)
Address = B+L1+L2
• Information about field types same for all
records in a file; stored in system catalogs.
• Finding i’th field does not require scan of
record.
Record Formats: Variable Length
• Two alternative formats (# fields is fixed):
F1
4
Field
Count
F2
$
F3
$
F4
$
$
Fields Delimited by Special Symbols
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.
Page Formats: Fixed Length Records
Slot 1
Slot 2
Slot 1
Slot 2
Free
Space
...
...
Slot N
Slot N
Slot M
N
PACKED
1 . . . 0 1 1M
number
of records
M ... 3 2 1
UNPACKED, BITMAP
number
of slots
* Record id = <page id, slot #>. In first alternative,
moving records for free space management changes rid;
may not be acceptable.
Page Formats: Variable Length Records
Rid = (i,N)
Page i
Rid = (i,2)
Rid = (i,1)
20
N
...
16
2
24
N
1 # slots
SLOT DIRECTORY
* Can move records on page without changing
rid; so, attractive for fixed-length records too.
Pointer
to start
of free
space
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)
File Organization
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.
Unordered (Heap) Files
• Simplest file structure contains records in no particular
order.
• As file grows and shrinks, disk pages are allocated and deallocated.
• 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.
Heap File Implemented as a List
Data
Page
Data
Page
Data
Page
Full Pages
Header
Page
Data
Page
Data
Page
Data
Page
Pages with
Free Space
• The header page id and Heap file name must be stored
someplace.
• Each page contains 2 `pointers’ plus data.
Heap File Using a Page Directory
Data
Page 1
Header
Page
Data
Page 2
DIRECTORY
Data
Page N
• 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!
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!
Index Structures
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 …)
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
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.
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.
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!
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.)
CLUSTERED
Index entries
direct search for
data entries
Data entries
UNCLUSTERED
Data entries
(Index File)
(Data file)
Data Records
Data Records
Tree-Structured Indexes
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.
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.
Page 1
Page 2
Index File
kN
k1 k2
Page 3
* Can do binary search on (smaller) index file!
Page N
Data File
B+ Tree: Most Widely Used Index
• Insert/delete at log F N cost; keep tree heightbalanced. (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.
Index Entries
(Direct search)
Data Entries
("Sequence set")
Example B+ Tree
• Search begins at root, and key comparisons
direct it to a leaf.
• Search for 5*, 15*, all data entries >= 24* ...
Root
13
2*
3*
5*
7*
14* 16*
17
24
19* 20* 22*
30
24* 27* 29*
* Based on the search for 15*, we know it is not in the tree!
33* 34* 38* 39*
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
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.
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.
Entry to be inserted in parent node.
(Note that 5 is
s copied up and
continues to appear in the leaf.)
5
2*
3*
5*
17
5
13
24
7*
8*
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.)
30
Example B+ Tree After Inserting 8*
Root
17
5
2*
3*
24
13
5*
7* 8*
14* 16*
19* 20* 22*
30
24* 27* 29*
33* 34* 38* 39*
 Notice that root was split, leading to increase in height.
 In this example, we can avoid split by re-distributing
however, this is usually not done in practice.
entries;
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.
Example Tree After (Inserting 8*, Then)
Deleting 19* and 20* ...
Root
17
5
2*
3*
27
13
5*
7* 8*
14* 16*
22* 24*
30
27* 29*
33* 34* 38* 39*
• Deleting 19* is easy.
• Deleting 20* is done with re-distribution.
Notice how middle key is copied up.
... And Then Deleting 24*
• Must merge.
• Observe `toss’ of
index entry (on right),
and `pull down’ of
index entry (below).
30
22*
27*
29*
33*
34*
38*
39*
Root
5
2*
3*
5*
7*
8*
13
14* 16*
17
30
22* 27* 29*
33* 34* 38* 39*
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
2* 3*
5* 7* 8*
13
14* 16*
17
30
20
17* 18*
20* 21*
22* 27* 29*
33* 34* 38* 39*
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
2* 3*
5* 7* 8*
13
14* 16*
20
17* 18*
20* 21*
22
30
22* 27* 29*
33* 34* 38* 39*
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.
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
3* 4*
Sorted pages of data entries; not yet in B+ tree
6* 9*
10* 11*
12* 13* 20* 22* 23* 31* 35* 36*
38* 41* 44*
Bulk Loading (Contd.)
Root
• Index entries for leaf
pages always
entered into rightmost index page just
above leaf level.
3*
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!
10
20
Data entry pages
6
4*
3* 4*
6* 9*
12
23
20
10
6* 9*
not yet in B+ tree
10* 11* 12* 13* 20*22* 23* 31* 35* 36* 38*41* 44*
Root
6
35
12
Data entry pages
not yet in B+ tree
35
23
38
10* 11* 12* 13* 20*22* 23* 31* 35* 36* 38*41* 44*
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.
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 different
nodes will contain different numbers of entries.
Even with fixed length fields, multiple records with the
same search key value (duplicates) can lead to variablesized data entries (if we use Alternative (3)).
Summary
• Tree-structured indexes are ideal for rangesearches, also good for equality searches.
• 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.
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.
Hash-Based Indexes
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 orthogonal to the indexing technique
• Hash-based indexes are best for equality
selections. Cannot support range searches.
• Static and dynamic hashing techniques exist;
Static Hashing
• # primary pages fixed, allocated sequentially,
never de-allocated; overflow pages if needed.
• h(k) mod M = bucket to which data entry with
key k belongs. (M = # of buckets)
h(key) mod N
key
0
2
h
N-1
Primary bucket pages
Overflow pages
Static Hashing (Contd.)
• Buckets contain data entries.
• Hash fn works on search key field of record r.
Must distribute values over range 0 ... M-1.
▫
▫
h(key) = (a * key + b) usually works well.
a and b are constants; lots known about how to tune
h.
• Long overflow chains can develop and degrade
performance.
▫
Extendible and Linear Hashing: Dynamic
techniques to fix this problem.
Extendible Hashing
• Situation: Bucket (primary page) becomes full. Why
not re-organize file by doubling # of buckets?
▫
▫
▫
▫
Reading and writing all pages is expensive!
Idea: Use directory of pointers to buckets, double # of
buckets by doubling the directory, splitting just the
bucket that overflowed!
Directory much smaller than file, so doubling it is much
cheaper. Only one page of data entries is split. No
overflow page!
Trick lies in how hash function is adjusted!
LOCAL DEPTH
Example
GLOBAL DEPTH
2
4* 12* 32* 16*
2
• Directory is array of size 4.
• To find bucket for r, take last
`global depth’ # bits of h(r);
we denote r by h(r).
▫
If h(r) = 5 = binary 101,
it is in bucket pointed to
by 01.
00
Bucket A
2
1*
5* 21* 13*
Bucket B
01
10
2
11
10*
Bucket C
2
DIRECTORY
15* 7* 19*
DATA PAGES

Insert: If bucket is full, split it (allocate new page, re-distribute).

If necessary, double the directory. (As we will see, splitting a
bucket does not always require doubling; we can tell by
comparing global depth with local depth for the split bucket.)
Bucket D
Insert h(r)=20 (Causes Doubling)
LOCAL DEPTH
2
32*16*
GLOBAL DEPTH
2
00
Bucket A
3
32* 16* Bucket A
GLOBAL DEPTH
2
3
1* 5* 21*13* Bucket B
01
000
2
1* 5* 21* 13* Bucket B
001
10
2
11
10*
Bucket C
15* 7* 19*
Bucket D
2
011
10*
Bucket C
101
2
110
15* 7* 19*
Bucket D
111
2
4* 12* 20*
010
100
2
DIRECTORY
LOCAL DEPTH
Bucket A2
(`split image'
of Bucket A)
3
DIRECTORY
4* 12* 20*
Bucket A2
(`split image'
of Bucket A)
Points to Note
• 20 = binary 10100. Last 2 bits (00) tell us r belongs in A
or A2. Last 3 bits needed to tell which.
▫
▫
Global depth of directory: Max # of bits needed to tell
which bucket an entry belongs to.
Local depth of a bucket: # of bits used to determine if an
entry belongs to this bucket.
• When does bucket split cause directory doubling?
▫
Before insert, local depth of bucket = global depth. Insert
causes local depth to become > global depth; directory is
doubled by copying it over and `fixing’ pointer to split
image page. (Use of least significant bits enables efficient
doubling via copying of directory!)
Directory Doubling
Why use least significant bits in directory?
 Allows for doubling via copying!
6 = 110
2
1
0
1
6*
6 = 110
3
00
10
000
000
001
100
2
010
1
011
01
6*
11
100
0
101
1
110
6*
00
6*
01
010
110
10
11
111
Least Significant
3
001
6*
101
011
111
vs.
Most Significant
6*
Comments on Extendible Hashing
• If directory fits in memory, equality search answered
with one disk access; else two.
▫
▫
▫
100MB file, 100 bytes/rec, 4K pages contains 1,000,000
records (as data entries) and 25,000 directory elements;
chances are high that directory will fit in memory.
Directory grows in spurts, and, if the distribution of hash
values is skewed, directory can grow large.
Multiple entries with same hash value cause problems!
• Delete: If removal of data entry makes bucket empty,
can be merged with `split image’. If each directory
element points to same bucket as its split image, can
halve directory.
Summary
• Hash-based indexes: best for equality searches, cannot
support range searches.
• Static Hashing can lead to long overflow chains.
• Extendible Hashing avoids overflow pages by splitting a
full bucket when a new data entry is to be added to it.
(Duplicates may require overflow pages.)
▫
▫
•
Directory to keep track of buckets, doubles periodically.
Can get large with skewed data; additional I/O if this does
not fit in main memory.
For hash-based indexes, a skewed data distribution is
one in which the hash values of data entries are not
uniformly distributed!
Comparing Storage Techniques
Cost Model for Our Analysis
We ignore CPU costs, for simplicity:
▫
▫
▫
▫
▫
B: The number of data pages
R: Number of records per page
D: (Average) time to read or write disk page
Measuring number of page I/O’s ignores gains of pre-fetching
a sequence of pages; thus, even I/O cost is only approximated.
Average-case analysis; based on several simplistic
assumptions.
* Good enough to show the overall trends!
Comparing File Organizations
•
•
•
•
•
Heap files (random order; insert at eof)
Sorted files, sorted on <age, sal>
Clustered B+ tree file, Alternative (1), search
key <age, sal>
Heap file with unclustered B + tree index on
search key <age, sal>
Heap file with unclustered hash index on
search key <age, sal>
Operations to Compare
•
•
•
•
•
Scan: Fetch all records from disk
Equality search
Range selection
Insert a record
Delete a record
Assumptions in Our Analysis
• Heap Files:
▫
Equality selection on key; exactly one match.
• Sorted Files:
▫
Files compacted after deletions.
• Indexes:
▫ Alt (2), (3): data entry size = 10% size of record
▫ Hash: No overflow buckets.

▫
80% page occupancy => File size = 1.25 data size
Tree: 67% occupancy (this is typical).

Implies file size = 1.5 data size
Assumptions (contd.)
• Scans:
▫ Leaf levels of a tree-index are chained.
▫ Index data-entries plus actual file scanned for
unclustered indexes.
• Range searches:
▫ We use tree indexes to restrict the set of data
records fetched, but ignore hash indexes.
Cost of Operations
(a) Scan
(b)
Equality
(c ) Range
(d) Insert
(e) Delete
(1) Heap
(2) Sorted
(3) Clustered
(4) Unclustered
Tree index
(5) Unclustered
Hash index
* Several assumptions underlie these (rough) estimates!
Cost of Operations
(a) Scan
(b) Equality
(c ) Range
(d) Insert (e) Delete
(1) Heap
BD
0.5BD
BD
2D
(2) Sorted
BD
Dlog 2B
D(log 2 B +
# pgs with
match recs)
(3)
1.5BD
Dlog F 1.5B D(log F 1.5B
Clustered
+ # pgs w.
match recs)
(4) Unclust. BD(R+0.15)
D(1 +
D(log F 0.15B
Tree index
log F 0.15B) + # pgs w.
match recs)
(5) Unclust. BD(R+0.125) 2D
BD
Hash index
Search
+ BD
Search
+D
Search
+BD
Search
+D
Search
+D
Search
+ 2D
Search
+ 2D
Search
+ 2D
Search
+ 2D
* Several assumptions underlie these (rough) estimates!
Choosing a File Organization
Understanding the Workload
• For each query in the workload:
▫
▫
▫
Which relations does it access?
Which attributes are retrieved?
Which attributes are involved in selection/join conditions? How
selective are these conditions likely to be?
• For each update in the workload:
▫
▫
Which attributes are involved in selection/join conditions? How
selective are these conditions likely to be?
The type of update (INSERT/DELETE/UPDATE), and the attributes th
are affected.
Choice of Indexes
• What indexes should we create?
▫
Which relations should have indexes? What
field(s) should be the search key? Should we
build several indexes?
• For each index, what kind of an index should it
be?
▫
Clustered? Hash/tree?
Choice of Indexes (Contd.)
• One approach: Consider the most important queries in turn.
Consider the best plan using the current indexes, and see if a
better plan is possible with an additional index. If so, create
it.
▫ Obviously, this implies that we must understand how a DBMS
evaluates queries and creates query evaluation plans!
▫ For now, we discuss simple 1-table queries.
• Before creating an index, must also consider the impact on
updates in the workload!
▫
Trade-off: Indexes can make queries go faster, updates slower.
Require disk space, too.
Index Selection Guidelines
• Attributes in WHERE clause are candidates for index keys.
▫ Exact match condition suggests hash index.
▫ Range query suggests tree index.
 Clustering is especially useful for range queries; can also help on equality
queries if there are many duplicates.
• Multi-attribute search keys should be considered when a WHERE
clause contains several conditions.
▫
▫
Order of attributes is important for range queries.
Such indexes can sometimes enable index-only strategies for
important queries.
 For index-only strategies, clustering is not important!
• Try to choose indexes that benefit as many queries as possible.
Since only one index can be clustered per relation, choose it based
on important queries that would benefit the most from clustering.
Examples of Clustered Indexes
• B+ tree index on E.age can be
used to get qualifying tuples.
How selective is the condition?
▫ Is the index clustered?
• Consider the GROUP BY query.
▫ If many tuples have E.age > 10,
using E.age index and sorting the
retrieved tuples may be costly.
▫ Clustered E.dno index may be
better!
▫
• Equality queries and duplicates:
▫
Clustering on E.hobby helps!
SELECT E.dno
FROM Emp E
WHERE E.age>40
SELECT E.dno, COUNT (*)
FROM Emp E
WHERE E.age>10
GROUP BY E.dno
SELECT E.dno
FROM Emp E
WHERE E.hobby=Stamps
Indexes with Composite Search Keys
• Composite Search Keys: Search on a
combination of fields.
▫
▫
Examples of composite key
indexes using lexicographic order.
11,80
11
12,10
12
Equality query: Every field value is
equal to a constant value. E.g. wrt
<sal,age> index:
12,20
 age=20 and sal =75
13,75
Range query: Some field value is not a
constant. E.g.:
<age, sal>
 age =20; or age=20 and sal > 10
• Data entries in index sorted by search
key to support range queries.
▫
▫
Lexicographic order, or
Spatial order.
10,12
20,12
75,13
name age sal
bob 12
10
cal 11
80
joe 12
20
sue 13
75
12
13
<age>
10
Data records
sorted by name
80,11
<sal, age>
Data entries in index
sorted by <sal,age>
20
75
80
<sal>
Data entries
sorted by <sal>
Composite Search Keys
• To retrieve Emp records with age=30 AND sal=4000, an
index on <age,sal> would be better than an index on age
or an index on sal.
Choice of index key orthogonal to clustering etc.
• If condition is: 20<age<30 AND 3000<sal<5000:
▫ Clustered tree index on <age,sal> or <sal,age> is best.
• If condition is: age=30 AND 3000<sal<5000:
▫ Clustered <age,sal> index much better than <sal,age>
index!
▫
• Composite indexes are larger, updated more often.
Index-Only Plans
SELECT E.dno, COUNT(*)
• A number of
queries can
<E.dno> FROM Emp E
GROUP BY E.dno
be answered
without
retrieving any
tuples from
<E.dno,E.sal> SELECT E.dno, MIN(E.sal)
one or more
FROM Emp E
Tree
index!
of the
GROUP BY E.dno
relations
involved if a <E. age,E.sal> SELECT AVG(E.sal)
suitable index
or
FROM Emp E
is available.
<E.sal, E.age> WHERE E.age=25 AND
E.sal BETWEEN 3000 AND 5000
Tree index!
Index-Only Plans (Contd.)
• Index-only plans
are possible if
the key is
<dno,age> or we
have a tree index
with key
<age,dno>
▫ Which is better?
▫ What if we
consider the
second query?
SELECT E.dno, COUNT (*)
FROM Emp E
WHERE E.age=30
GROUP BY E.dno
SELECT E.dno, COUNT (*)
FROM Emp E
WHERE E.age>30
GROUP BY E.dno
Index-Only Plans (Contd.)
<E.dno>
• Index-only
plans can also
be found for
queries
involving more
than one table;
more on this
later.
SELECT D.mgr
FROM Dept D, Emp E
WHERE D.dno=E.dno
<E.dno,E.eid>
SELECT D.mgr, E.eid
FROM Dept D, Emp E
WHERE D.dno=E.dno
Summary
• Many alternative file organizations exist, each appropriate in
some situation.
• If selection queries are frequent, sorting the file or building an
index is important.
▫
▫
Hash-based indexes only good for equality search.
Sorted files and tree-based indexes best for range search; also
good for equality search. (Files rarely kept sorted in practice; B+
tree index is better.)
• Index is a collection of data entries plus a way to quickly find
entries with given key values.
Summary (Contd.)
• Data entries can be actual data records, <key, rid> pairs,
or <key, rid-list> pairs.
▫
Choice orthogonal to indexing technique used to locate data
entries with a given key value.
• Can have several indexes on a given file of data records,
each with a different search key.
• Indexes can be classified as clustered vs. unclustered,
primary vs. secondary, and dense vs. sparse. Differences
have important consequences for utility/performance.
Summary (Contd.)
• Understanding the nature of the workload for the application,
and the performance goals, is essential to developing a good
design.
▫
What are the important queries and updates? What
attributes/relations are involved?
• Indexes must be chosen to speed up important queries (and
perhaps some updates!).
▫
▫
▫
▫
▫
Index maintenance overhead on updates to key fields.
Choose indexes that can help many queries, if possible.
Build indexes to support index-only strategies.
Clustering is an important decision; only one index on a given
relation can be clustered!
Order of fields in composite index key can be important.