overview of storage and indexing

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Overview of Storage and Indexing

Chapter 8(part 1)

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Motivation DBMS stores vast quantities of data Data is stored on external storage devices and

fetched into main memory as needed for processing

Page is unit of information read from or written to disk. (in DBMS, a page may have size 8KB or more).

Data on external storage devices : Disks: Can retrieve random page at fixed cost

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

Tapes: Can only read pages in sequenceCheaper than disks; used for archival storage

Cost of page I/O dominates cost of typical database operations

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Files versus Indices

File organization : Method of arranging a file of records on external

storage. Record id (rid) is sufficient to physically locate

record

Indexes : Indexes are data structures that allow to find

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

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File Organizations

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 to optimize certain kinds of retrieval operations.

• Speed up searches for a subset of records, based on values in certain (“search key”) fields

• Updates are much faster than in sorted files.

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Alternatives for Data Entry k* in Index Data Entry : Records stored in index file

Given search key value k, provide for efficient retrieval of all data entries k* with value k.

In a data entry k* , alternatives include that we can store: alternative 1: Full data record with key value k, or alternative 2: <k, rid of data record with search key value k>,

or alternative 3: <k, list of rids of data records with search key k>

Choice of above 3 alternative data entries is orthogonal to indexing technique used to locate data entries. Example indexing techniques: B+ trees, hash-based structures,

etc.

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Alternatives for Data Entries Alternative 1: Full data record with key

value k

Index structure is 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, this implies size of auxiliary information in index is also large.

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Alternatives for Data Entries Alternatives 2 (<k, rid>) and 3 (<k, list-of-

rids>): Data entries typically much smaller than data

records.

Comparison: Both better than Alternative 1 with large data

records, especially if search keys are small.

Alternative 3 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 index:

If search key contains primary key, then called primary index. Clustered vs. unclustered index :

If order of data records is the same as, or `close to’, order of data entries, then called clustered index.

Claim : Alternative 1 implies clustered. True ? Claim : In practice, clustered also implies Alternative

1 (since sorted files are rare). Observation 1:

A file can be clustered on at most one search key. Observation 2:

Cost of retrieving data records through index varies greatly based on whether index is clustered or not !!

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Index Clustered vs Unclustered

Observation 1: Alternative 1 implies clustered. True ?

Observation 2: In practice, clustered also implies Alternative 1

(since sorted files are rare). Observation 3:

A file can be clustered on at most one search key. Observation 4:

Cost of retrieving data records through index varies greatly based on whether index is clustered or not !!

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Clustered vs. Unclustered Index

Index entries

Data entries

direct search for

(Index File)

(Data file)

Data Records

data entries

Data entries

Data Records

CLUSTERED UNCLUSTERED

Suppose Alternative (2) is used for data entries,

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Clustered vs. Unclustered Index

Use Alternative (2) for data entries Data records are stored in Heap file.

To build clustered index, first sort the Heap file Overflow pages may be needed for inserts. Thus, order of data recs is close to (not identical to) 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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B+ Tree Indexes

Index leaf pages contain data entries, and are chained (prev & next) Index 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: 29*? 28*? All > 15* and < 30* Insert/delete: Find data entry in leaf, then

change it.

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

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 search key fields of r. No need for “index entries” in this scheme due to one-

level index file

Good for equality selections.

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Cost Model for Our Analysis

Notes: We ignore CPU costs, for simplicity. Measuring number of page I/Os ignores gains of

pre-fetching a sequence of pages Thus even I/O cost is only approximated. Average-case analysis; based on simplistic

assumptions.

Good enough to show overall trends!

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Cost Model for Our Analysis

Variables : B: The number of data pages R: Number of records per page D: (Average) time to read or write disk page

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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> (Alt 2)

Heap file with unclustered hash index

on search key <age, sal> (Alt 2)

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Operations to Compare

Scan: Fetch all records from disk Equality search Range selection Insert a record Delete a record

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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 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 set of data records fetched, but ignore hash indexes.

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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!

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Heap File

Scan Equality Range Insert Delete

BD 0.5BD BD 2D Search + D

On average scan half the file.

Uniform distribution.

Record can appear anywhere in the file.

Add at the end.

Fetch last page + add record + write page back

B: The number of data pagesR: Number of records per pageD: (Average) time to read or write disk page

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Sorted File


BD Dlog2B D(log2B+#pgs with

match records)

Search + BD

Search + BD

Result is sorted.

Equality selection matches the sort order.

Binary search.

Matching middle of file.

Read later half and write.

Same with insert.


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Clustered B+ Tree FilesScan Equality Range Insert Delete

1.5BD DlogF1.5B D(logF1.5B +#pgs

with match

records)

Search + D

Search + D

Search + one write

same


(1) Pages in clusered file are 67% occupancy(2) # pages = 1.5B(3) F (fan out)

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Heap File with UnClustered Tree Index


0.15BD+

RBD

D(1+logF0.15B)

D(logF0.15B +#pgs with

match records)

D(3 +logF0.15B)

Search + 2D

Read data entry: 0.15BD

Fetch the employee record for each data entry in index(unclustered)

Insert in heap file 2D

Find right leaf page logF0.15B, add new data entry, write back D


(1) Pages in clusered file are 67% occupancy(2) F (fan out)(3) Index is a tenth the size of an employee data record(4) # pages = 0.1(1.5B) = 0.15B

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Heap File with (UnClustered) Hash Index


0.125BD+

RBD

2D BD 4D Search + 2D

Read data entry: 0.15BD

Fetch the employee record for each data entry in index(unclustered)

Fetch data entry from index file

Fetch data record from file

Hash structure offers no help

Scan entire heap file

Insert record into heap file 2D

Insert into index page and write back 2D

Delete index D

Delete data page D


(1) Pages in clusered file are 80% occupancy(2) F (fan out)(3) Index is a 10th the size of an employee data record(4) # pages = 0.1(1.25B) = 0.125B

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Cost of Operations (a) Scan (b) Equality (c ) Range (d) Insert (e) Delete

(1) Heap BD 0.5BD BD 2D Search +D

(2) Sorted BD Dlog 2B D(log 2 B + # pgs with match recs)

Search + BD

Search +BD

(3) Clustered

1.5BD Dlog F 1.5B D(log F 1.5B + # pgs w. match recs)

Search + D

Search +D

(4) Unclust. Tree index

BD(R+0.15) D(1 + log F 0.15B)

D(log F 0.15B + # pgs w. match recs)

Search + 2D

Search + 2D

(5) Unclust. Hash index

BD(R+0.125) 2D BD Search + 2D

Search + 2D


D(3 +

logF0.15B)

Search + 2D

4D Search + 2D

No one file organization is uniformly superior in all situations !!!

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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

Data entries can be : actual data records, <key, rid> pairs, or <key, rid-list> pairs.

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,

Differences have important consequences for utility/performance of query processing

overview of storage and indexing

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