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Indexes on Sequential Files

Source: our textbook, slides by Hector Garcia-Molina

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How to Represent a Relation

Suppose we scatter its records arbitrarily among the blocks of the disk

How to answer SELECT * FROM R? Scan every block:

ridiculously slow would require lots of overhead info in

each block and each record header

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How to Represent a Relation

Reserve some blocks for the relation No need to scan entire disk How to answer SELECT * FROM R

WHERE cond ? Scan all the records in the reserved

blocks Still ridiculously slow

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Indexes Use indexes -- special data

structures -- that allow us to find all the records that satisfy a condition "efficiently"

Possible data structures: simple indexes on sorted files secondary indexes on unsorted files B-trees hash tables

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Sorted Files Sorted file: records (tuples) of the

file (relation) are in sorted order of the field (attribute) of interest.

This field might or might not be a key of the relation.

This field is called the search key. A sorted file is also called a

sequential file.

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Index on Sequential File An index is another file containing

key-pointer pairs of the form (K,a) K is a search key a is an address (pointer) The record at address a has search

key K Particularly useful when the search

key is the primary key of the relation

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Dense Indexes An index with one entry for every key in

the data file What's the point? Index is much smaller than data file when

record contains much more than just the search key

If index is small enough to fit in main memory, record with a certain search key can be found quickly: binary search in memory, followed by only one disk I/O

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Example of a Dense IndexSequential File

2010

4030

6050

8070

10090

Dense Index102030405060708090

100110120

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Some Numbers relation with 1,000,000 tuples block size is 4096 bytes 10 records per block thus 100,000 blocks, > 400 Mbytes key field is 30 bytes pointer is 8 bytes thus at least 100 key-pointer pairs per block thus dense index size is 10,000 blocks, about 40

Mbytes since log(10,000) = 13, takes at most 14 disk

I/O's for a search

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Sparse Index Uses less space than a dense index Requires more time to find a

record with a given key In a sparse index, there is just one

(key,pointer) pair per data block. The key is for the first record in the

block.

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Sparse Index ExampleSequential File

2010

4030

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10090

Sparse Index1030507090

110130150170190210230

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Using a Sparse Index To find the record with key K,

search the index for the largest key ≤ K

Use binary search to do this Retrieve the indicated data block Search the block for the record

with key K

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Comparing Sparse and Dense Indexes

Sparse index uses much less space In the previous numeric example,

sparse index size is now only 1000 index blocks, about 4 Mbytes

Dense index, unlike sparse, lets us answer "is there a record with key K?" without having to retrieve a data block

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Multiple Levels of Index Make an index for the index Can continue this idea for more

levels, but usually only two levels in practice

Second and higher level indexes must be sparse, otherwise no savings

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Two-Level Index ExampleSequential File

2010

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8070

10090

Sparse 2nd level1030507090110130150170190210230

1090

170250

330410490570

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Numeric Example Again Suppose we put a second-level index on

the first-level sparse index Since first-level index uses 1000 blocks

and 100 key-pointer pairs fit per block, we need 10 blocks for second-level index

Very likely to keep the second-level index in memory

Thus search requires at most two disk I/O's (one for block of first-level index, one for data block)

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Duplicate Search Keys What if more than one record has a

given search key value? (Then the search key is not a key of the relation.)

Solution 1: Use a dense index and allow duplicate search keys in it.

To find all data records with search key K, follow all the pointers in the index with search key K

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Solution 1 Example

1010

2010

3020

3030

4540

10101020

20303030

1010

2010

3020

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4540

10101020

20303030

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Duplicate Search Keys with Dense Index

Solution 2: only keep record in index for first data record with each search key value (saves some space in the index)

To find all data records with search key K, follow the one pointer in the index and then move forward in the data file

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Solution 2 Example

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10203040

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Duplicate Search Keys with Sparse Index

Recall that index has an entry for just the first data record in each block

To find all data records with key K: find last entry (E1) in index with key ≤ K move toward front of index until reaching

entry (E2) with key < K Check data blocks pointed to by entries

from E2 to E1 for records with search key K

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Dupl. Keys w/ Sparse Index

1010

2010

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10102030

care

ful i

f loo

king

for 2

0 or

30!

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Variation on Previous Scheme

Index entry for a data block holds smallest search key that is new (did not appear in a previous block)

If there is no new search key in that block, then index entry holds the lone search key in the block

To find all data record with key K: search index for first entry whose key is either

K, or < K but next key is > K if a record with key K is in that block then scan

forward from there

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Variation Example

1010

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4540

10203030

shouldthis be40?

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Inserting and Deleting Data

Recall three main techniques: create/delete overflow blocks

overflow blocks do not have entries in a sparse index

may be able to insert new blocks in sequential order new block needs an entry in a sparse index changing an index can create same problems

make room in a full block by sliding some data to an adjacent block; combine adjacent blocks if they get too empty

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General Strategy When data file changes, index must

adapt Details depend on whether index is

sparse or dense and how data file modifications are implemented

Index file is itself sequential, so same strategies as for modifying data files can be applied to index files

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Effects of Actions on IndexAction Dense Index Sparse IndexCreate empty overflow block

none none

Delete empty overflow block

none none

Create empty (main) block

none insert

Delete empty (main) block

none delete

Insert record insert maybe updateDelete record delete maybe updateSlide record update maybe update

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Explanations for Actions create/destroy empty overflow block has

no effect on dense index since it refers to records sparse index since it refers to main records

create/destroy empty main block: no effect on dense index as above insert/delete entry in sparse index

insert/delete/slide record: insert/delete/update entry in dense index only change sparse index if affects first

record in block

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Deletion from sparse index

2010

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10305070

90110130150

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Deletion from sparse index

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10305070

90110130150

– delete record 40

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Deletion from sparse index

2010

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10305070

90110130150

– delete record 30

4040

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Deletion from sparse index

2010

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10305070

90110130150

– delete records 30 & 40

5070

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Deletion from dense index

2010

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10203040

50607080

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Deletion from dense index

2010

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10203040

50607080

– delete record 30

4040

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Insertion, sparse index case

2010

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10304060

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Insertion, sparse index case

2010

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10304060

– insert record 34

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• our lucky day! we have free space where we need it!

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Insertion, sparse index case

2010

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10304060

– insert record 15

1520

3020

• Illustrated: Immediate reorganization• Variation:

– insert new block (chained file)– update index

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Insertion, sparse index case

2010

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10304060

– insert record 2525

overflow blocks(reorganize later...)

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Insertion, dense index case

• Similar• Often more expensive . . .