1

Overview of Storage and Indexing

Chapter 8

“How index-learning turns no student paleYet holds the eel of science by the tail.”

-- Alexander Pope (1688-1744)

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Why Concerning Storage and Indexing?

DB design using logical models (ER/Relational). Appropriate level for designers to begin with Provide independence from implementation details

Performance: another major factor in user satisfaction Depends on

• Efficient data structures for data representation• Efficiency of system operation on those structures

Disks contains data files and system files including dictionary and index files

Disk access: one of the most critical factor in performance.

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Subjects to be Discussed Disks: Can retrieve random page, but reading

several consecutive pages is much cheaper than reading them in random order

Buffer manager: Stages pages from external storage to main memory buffer pool. File and index layers make calls to the buffer manager.

File organization: Method of arranging a file of records on external storage. Record id (rid) is sufficient to physically locate record Indexes are data structures that allow us to find the

record ids of records with given values in index search key fields

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Storage Hierarchy

DBMS stores information on some storage medium Primary storage: can be operated directly by CPU. Secondary storage:

• larger capacity, lower cost, slower access• cannot be operated directly by CPU – must be copied

to primary storage Secondary storage has major implications for DBMS

design READ: transfer data to main memory WRITE: transfer data from main memory. Both transfers are high-cost operations, relative to in-

memory operations, so must be planned carefully

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Why Not Store Everything in Main Memory?

Cost and size Main memory is volatile: What’s the problem? Typical storage hierarchy:

Factors: access speed, cost per unit, reliability Cache and main memory (RAM) for currently

used data: fast but costly Flash memory: limited number of writes (and

slow), non-volatile, disk-substitute in embedded systems

Disk for the main database (secondary storage). Tapes for archiving older versions of the data

(tertiary storage).

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Disks

Secondary storage device of choice. 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!

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Components of a Disk

Platters

The platters spin

Spindle

The arm assembly is moved in or out to position a head on a desired track. Tracks under heads make a cylinder (imaginary!).

Disk head

Arm movement

Arm assembly

Only one head reads/writes at any one time.

Tracks

Sector

Block size is a multiple of sector size (which is fixed).

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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 less than 1msec per 4KB page

Key to lower I/O cost: reduce seek/rotation delays

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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!

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Platters

Spindle

Disk head

Arm movement

Arm assembly

Tracks

Sector

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RAID Redundant Arrays of Independent Disks Disk Array: Arrangement of several disks that

gives abstraction of a single, large disk. Goals: Increase performance and reliability. Two main techniques: parallelism and

redundancy Data striping: Data is partitioned; size of a partition

is called the striping unit. Partitions are distributed over multiple disks.

Redundancy: More disks -> more failures. Redundant information allows reconstruction of data if a disk fails.

RAID levels: level 0 – level 6

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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

Highly desirable that a request for a sequence of pages to be satisfied by allocating the pages sequentially on disk.

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Structure of a DBMS

A typical DBMS has a layered architecture.

The figure does not show the concurrency control and recovery components.

This is one of several possible architectures; each system has its own variations.

Query Optimizationand Execution

Relational Operators

Files and Access Methods

Buffer Management

Disk Space Management

DB

These layers must consider concurrencycontrol and recovery

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Buffer Management in a DBMS

Data must be in RAM for DBMS to operate on it. Table of <frame#, pageid> pairs is maintained.

DB

MAIN MEMORY

DISK

disk page

free frame

Page Requests from Higher Levels

BUFFER POOL

choice of frame dictatedby replacement policy

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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!

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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 require additional I/O

when a frame is chosen for replacement. Why?

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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).

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DBMS vs. OS File System OS does disk space & buffer mgmt: why not

let OS manage these tasks?

Differences in OS support: portability issues Some limitations, e.g., files can’t span disks. Buffer management in DBMS requires

different abilities pin a page in buffer pool, force a page to disk

(important for implementing CC & recovery), adjust replacement policy, and pre-fetch pages

based on access patterns in typical DB operations.

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File Organizations

Several 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.

Indexed files: For efficient searching Which organization is best? How can you tell?

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Efficient Searching

Additional structures to help searching Associated with data files to search for records

based on certain field (search key) values For direct record locating without sequential

search.

Indexes: Data structures to organize records via trees or hashing.

• Like sorted files, they speed up searches for a subset of records

• Updates are much faster than in sorted files.

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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 blocks 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!

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Assumptions used for Analysis

Single record insert and delete. Heap Files:

Equality selection on key; exactly one match. Insert always at end of file.

Sorted Files: Files compacted after deletions. Selections on sort field(s).

Hashed Files: No overflow buckets, 80% page occupancy.

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Cost of Operations

Heap File

Sorted File

Hashed File

Scan all recs BD BD 1.25 BD

Equality Search 0.5 BD D log2B D

Range Search BD D (log2B + # of pages with matches)

1.25 BD

Insert 2D Search + BD 2D

Delete Search + D Search + BD 2D

Several assumptions underlie these (rough) estimates!

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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 quickly.

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B+ Tree Indexes

Leaf pages contain data entries, and are chained (prev & next) Non-leaf pages have index entries; only used to direct searches:

P0 K 1 P 1 K 2 P 2 K m P m

index entry

Non-leaf

Pages

Pages (Sorted by search key)

Leaf

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Example B+ Tree

Find 28*? 29*? All > 15* and < 30* Insert/delete: Find data entry in leaf, then

change it. Need to adjust parent sometimes. And change sometimes bubbles up the tree

2* 3*

Root

17

30

14* 16* 33* 34* 38* 39*

135

7*5* 8* 22* 24*

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27* 29*

Entries < 17 Entries >= 17

Note how data entriesin leaf level are sorted

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Hash-Based Indexes

Good for equality selections. Index is a collection of buckets.

Bucket = primary page plus zero or more overflow pages.

Buckets contain data entries. Hashing function h: h(r) = bucket in

which (data entry for) record r belongs. h looks at the search key fields of r. No need for “index entries” in this scheme.

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Static Hashing # primary pages fixed, allocated

sequentially, never de-allocated; overflow pages if needed.

h(k) mod N = bucket to which data entry with key k belongs. (N = # of buckets)

h(key) mod N

hkey

Primary bucket pages Overflow pages

10

N-1

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Index What is an index? An index on a file speeds up selections on

the search key fields used for the index. Any subset of the fields of a relation can be the

search key for an index on the relation? Is search key 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 records with

key value k quickly.

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Index file and Data File Example: ``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. Idea: Create an `index’ file.

Can do binary search on (smaller) index file!

Page 1 Page 2 Page NPage 3 Data File

k2 kNk1 Index File

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Data Entry k* in Index A data entry k* refers to the records stored

in an index file with search key value k What does it contain? It contains enough information to locate data

record with search key value k Idea:

• Efficiently search an index with search key value k to find the data entries

• Use them to obtain the desired data records

For a given search key value k, will there be exactly 0 or 1 data record?

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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

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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. Why?

Otherwise, data records are duplicated, leading to redundant storage and potential inconsistency.

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Alternatives for Data Entries (Contd.) Alternatives 2 and 3:

When are they better than Alternative 1? Data entries typically much smaller than data

records. So, they are better than Alternative 1 with large data records, especially if search keys are small.

Compare Alternatives 2 and 3 -- which one is better?

Alternative 3 is more compact than Alternative 2, but leads to variable sized data entries even if search keys are of fixed length.

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Index Classification

Primary vs. secondary: If search key contains primary key, then called primary index. Different defs in other books Unique index: Search key contains a candidate

key.

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Dense vs Sparse Index Dense index: one

index entry per search key value.

Sparse index: index records for only some of the records Every sparse index is

clustered! Sparse indexes are

smaller Which one is faster? Which one has less

overhead?

Ashby, 25, 3000

Smith, 44, 3000

Ashby

Cass

Smith

22

25

30

40

44

44

50

Sparse Indexon

Name Data File

Dense Indexon

Age

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Bristow, 30, 2007

Basu, 33, 4003

Cass, 50, 5004

Tracy, 44, 5004

Daniels, 22, 6003

Jones, 40, 6003

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Clustered Index 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 Can a file be clustered on with more than one search

key? Can non-key field become clustering index? Cost of retrieving data records through index varies

greatly based on whether index is clustered or not. Why? If the index is clustered, rids of qualifying data entries

point to a contiguous collection of records, and we need to retrieve only a few data pages.

If unclustered, each qualifying data entry could contain a rid that points to a distinct data page, leading to I/O

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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

Data entries

direct search for

(Index File)

(Data file)

Data Records

data entries

Data entries

Data Records

CLUSTERED UNCLUSTERED

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Understanding the Workload Why necessary? 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 that are affected.

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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 or not? Dense or sparse? Hash/tree?

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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.

Before creating an index, must also consider the impact on updates in the workload! Is there a trade-off for using index between

updates and queries? Trade-off: Indexes can make queries go faster,

updates slower. Require disk space, too.

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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.

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.

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Examples of Clustered Indexes

Tree or hashing? B+ tree index on E.age can be used

to get qualifying tuples. Things to consider:

How selective is the condition? If 99% are over 40, is index useful? If 10%, is an index useful?

Depends on whether the index is clustered If unclustered, it can be more expensive

than sequential scan with only 10%

SELECT E.dnoFROM Emp EWHERE E.age>40

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Examples of Clustered Indexes

Consider the GROUP BY query: using age as an index ---- is it effective?

If many tuples have E.age > 20, using E.age index and sorting the retrieved tuples may be costly.

Especially bad if this index is not clsutered

Clustered E.dno index may be better!SELECT E.dno, COUNT (*)FROM Emp EWHERE E.age>20GROUP BY E.dno

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Examples of Clustered Indexes

Clustering is important for an index on a search key that is not a candidate key

Equality queries and duplicates: Clustering on E.hobby helps!

What if WHERE E.eid=554 instead of WHERE E.hobby=Stamps?

Does clustered index helpful in this case?

SELECT E.dnoFROM Emp EWHERE E.hobby=Stamps

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Indexes with Composite Search Keys

Composite Search Keys: Search on a combination of fields. Equality query: Every field

value is equal to a constant value. E.g. wrt <sal,age> index:

• age=12 and sal =75 Range query: Some field value

is not a constant. E.g.:• age =12; or age=12 and sal >

10

Data entries in index sorted by search key to support range queries.

sue 13 75

bob

cal

joe 12

10

20

8011

12

name age sal

<sal, age>

<age, sal> <age>

<sal>

12,20

12,10

11,80

13,75

20,12

10,12

75,13

80,11

11

12

12

13

10

20

75

80

Data recordssorted by name

Data entries in indexsorted by <sal,age>

Data entriessorted by <sal>

Examples of composite keyindexes using lexicographic order.

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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 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.

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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.

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Summary (Contd.)

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.

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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. 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.

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Exercise Emp (eid: int, salary:int, age: real, did: int)

eid is the key, and there’s a clustered index on eid and an unclustered index on age

1. Why not making age another clustered index?

2. How will you use indexes to enforce the constraint that eid is a key?

3. Give an example of a query that can be speeded up because of the available indexes.

4. Give an example that is neither speeded up nor slowed down by the indexes.

5. Can there be an update that can be slowed down because of the indexes?