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# Chap.10 Indexed Sequential File Access and Prefix B+ Trees - PowerPoint PPT Presentation

File Structures by Folk, Zoellick, and Ricarrdi. Chap.10 Indexed Sequential File Access and Prefix B+ Trees. 서울대학교 컴퓨터공학부 객체지향시스템연구실 SNU-OOPSLA-LAB 교수 김 형 주. Chapter Objectives. Introduce indexed sequential files

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### Chap.10 Indexed Sequential File Access and Prefix B+ Trees

서울대학교 컴퓨터공학부

객체지향시스템연구실

SNU-OOPSLA-LAB

교수 김 형 주

SNU-OOPSLA Lab.

• Introduce indexed sequential files

• Describe operations on a sequence set of blocks that maintains records in order by key

• Show how an index set can be built on top of the sequence set to produce an indexed sequential file structure

• Introduce the use of a B-tree to maintain the index set, thereby introducing B+ trees and simple prefix B+ trees

• Illustrate how the B-tree index in a simple prefix B+ tree can be of variable order, holding a variable number of separators

• Compare the strengths and weakness of B+ trees, simple prefix B+ trees, and B-trees

SNU-OOPSLA Lab.

• 10.1 Indexed Sequential Access

• 10.2 Maintaining a Sequence Set

• 10.3 Adding a Simple Index to the Sequence Set

• 10.5 The Contents of the Index: Separators Instead of Keys

• 10.6 The Simple Prefix B+ Tree Maintenance

• 10.7 Index Set Block size

• 10.8 Internal Structure of the Index Set Blocks: A variable-order B-Tree

• 10.10 B+ Trees

• 10.11 B-Trees, B+ Trees, and Simple Prefix B+ Trees in Perspective

SNU-OOPSLA Lab.

• Two alternative views

• indexed : records are indexed by keys

• no good for sequential processing

• sequential : records can be accessed sequentially

• not good for access, insert, delete records in random order

• In chap 9, we see B tree and now we want derive Indexed + Sequential ==> B+ tree with help of the idea of the sequence set

• Sequential file ==> Indexed Sequential file ==> B+ tree

• Indexed-Sequential file = Indexed Sequential Access Method (ISAM)

SNU-OOPSLA Lab.

main memory

a

secondary memory

61

b

c

10

20

50

61

101

d

e

f

g

h

i

1

3

10

11

20

30

40

45

51

55

57

65

70

101

120

150

A

B

A

C

D

D

C

A

A

D

B

E

B

C

A

D

part description records

50

60

61

primary key

PART #

D

B

A

PART-Type

Example : Indexed sequential structure (when using overflow chain)

Overview : ISAM File

SNU-OOPSLA Lab.

• Compared with ordered relative file

• Ordered on a key, like ordered relative file

• Can be accessed by an index, structure that contains information on where a record with a given key is located (usually intermingled with blocks of records)

• Tree search of an index replaces binary search of ordered relative files

SNU-OOPSLA Lab.

Block

Data

Block

Data

Block

Data

Block

. . .

Overflow

Data

Block

Overflow

Data

Block

Overflow

Data

Block

Indexed Sequential Files

• Block types

• Index Block

• Primary Data Block

• Overflow Data Block

SNU-OOPSLA Lab.

• Retrieve parts_file where part# = 60

• Primary Key search : nodes R,a,b,g accessed

• 3 primary block access, 1 overflow block accessed

• Retrieve parts_file where part# = 101 and part_type = C (overqualified)

• Primary Key search : nodes R,a,c,h accessed

• 3 primary block accesses

• Block “access”es are really block fetches. The blocks may be in main memory buffers so that actual block accesses aren’t performed

SNU-OOPSLA Lab.

• Retrieve part_file where part#= 101 or part_type = C

• Scan : node R,d,e,f,g,h,I accessed

• 6 primary block “accesses”

• overflow block “accesses”

SNU-OOPSLA Lab.

2

3

R

a

61

b

c

10

20

50

61

101

d

e

f

g

h

i

1

3

10

11

20

30

40

45

51

55

57

65

70

101

120

150

A

B

A

C

D

D

C

A

A

D

B

E

B

C

A

D

50

60

61

D

B

A

Retrieval of Indexed sequential structure

SNU-OOPSLA Lab.

• (Step 1) Locate data level node via key search in which to insert record

• (Step 2) Determine if record is to be inserted into primary block or overflow in order to maintain primary key order sequence of records

• (Step 3a) If record is to be placed in primary block and block is not full, shift all records with higher-valued primary keys to the right and place new record into vacated slot. STOP.

SNU-OOPSLA Lab.

• (Step 3b) If record is to be placed in primary block and block is full, place record of the block with highest valued primary key so that it is the first record on the overflow chain (move one record to the overflow chain) . Primary block is now not full. Go to Step 3a.

• (Step 4) If record is to be placed in overflow chain, place record in appropriate position on overflow chain so that primary key sequencing is maintained. STOP.

SNU-OOPSLA Lab.

150

insert i

A

D

Yields(step 3a)

130

120

130

150

insert

E

A

E

D

insert

180

120

130

150

180

Yields(step 4)

C

A

E

D

C

110

110

120

130

150

180

insert

Yields(step 3b)

F

F

A

E

D

C

170

insert

110

120

130

150

170

180

Yields(step 4)

G

F

A

E

D

G

C

Example : Insertion

SNU-OOPSLA Lab.

• (Step 1) Locate record to delete by primary key search

• (Step 2) If record is in primary block, free its slot and shift all records in the block with higher-valued primary keys to the left. STOP

• (Step 3) If record is in overflow, remove it from overflow chain. STOP

SNU-OOPSLA Lab.

110

130

150

170

180

remove

yields

A

F

E

D

G

C

150

110

130

170

180

remove

yields

D

F

E

G

C

Example : Deletion

SNU-OOPSLA Lab.

• (Step 1) Locate record to update by primary key search

• (Step 2) If primary key was not altered, simply replace stored copy of record with the updated copy. STOP.

• (Step 3) If primary keywas altered, delete(remove) the located record. Insert updated record just as if were a new record. STOP.

SNU-OOPSLA Lab.

• Reading records out of old file in the primary key order

• Building new indexed sequential structure with no records in overflow. (file creation)

• Reorganization is really hectic !!!

• Definitions

SNU-OOPSLA Lab.

secondary memory

45

• 70

3

11

30

45

120

1

3

10

11

20

30

40

45

10

120

150

A

B

A

C

D

D

C

A

C

A

D

51

57

61

70

50

51

55

57

60

61

45

65

70

D

A

D

B

B

A

E

B

Example : Reorganization

SNU-OOPSLA Lab.

• (Step 1) Using a specified initial loading factor LF, pack LF records per node and create the data level of the new indexed sequential file structure. (Last node on data level will have from 1 to LF records in it)

• (Step 2) Build consecutive levels of index nodes until a level is reached where there is only a single node. The root node is created and is placed on the next higher level blocks of index are to be packed as full as possible. Stop.

SNU-OOPSLA Lab.

10.2 Maintaining a Sequence Set

• A sequence set (similar terms: ordered file, sequential set)

• a set of records in physical order by key

• Sequence set + Simple Index ===> Simple Prefix B+ Tree

• The Use of Blocks

• We want to rule out sorting and resorting of the sequence set

• insertion of records into block : overflow -> split

• deletion of records : underflow -> redistribution, concatenation

• costs for avoidance of sorting

• more space overhead (internal fragmentation in a block)

• -> redistribution in place of splitting, two-to-three splitting

• the maximum guaranteed extent of physical sequentiality is within a block -> choice of block size

SNU-OOPSLA Lab.

Block splitting & concatenation(1)

Block1

Block2

BYNUM...CARSON...COLE...DAVIS...

Block3

DENVER...ELLIS...

(a)Initial blocked sequence set

Block1

Block2

BYNUM...CARSON...CARTER...

Block3

DENVER...ELLIS...

Block4

COLE...DAVIS...

(b)Sequence set after insertion of CARTER record

- block 2 splits, and the contents are divided

between blocks 2 and 4

SNU-OOPSLA Lab.

(continued....)

Block splitting & concatenation(2)

Block1

Block2

BYNUM...CARSON...CARTER...

Block3

Available

for use

Block4

COLE...DENVER...ELLIS...

(c)Sequence set after deletion of DAVIS record

- block 4 is less than half full, so it is concatenated

with block3

SNU-OOPSLA Lab.

Issue: Choice of Block Size

• Block : basic unit for I/O

• The maximum guaranteed extent of physical sequentiality

• Two considerations

• several blocks should be in RAM at once

• e.g. for split or concatenation, at least two blocks in RAM

• reading/writing a block should not be very long

• Cluster :- the minimum number of sectors allocated at a time

- the minimum size of a file

• Reasonable suggestion: block size == cluster size

• can access a block without seeking within a cluster

SNU-OOPSLA Lab.

• An efficient way to locate some specific block containing a particular record, given the record’s key

• build index records containing the key for the last record in a block

• Possible Index Structures

• simple index

• binary search of the index

• works well while the entire index is in RAM

• B+ tree

• B-tree index + a sequence set with actual records

SNU-OOPSLA Lab.

-BERNE

BOLEN

-CAGE

CAMP

-DUTTON

EMBRY

-EVANS

FABER

-FOLK

FOLKS

1

2

3

4

5

6

Simple index

Key

Block Number

BERNE

CAGE

DUTTON

EVANS

FOLK

1

2

3

4

5

6

SNU-OOPSLA Lab.

• Need not to have actual keys in the index set

• Our real need is separators

• Separator - distinguishes between 2 blocks

• among many candidates, shortest separator is preferable

• there is not always a unique shortest separator

SNU-OOPSLA Lab.

Separators:

BO

CAM

E

F

FOLKS

-BERNE

BOLEN

-CAGE

CAMP

-DUTTON

EMBRY

-EVANS

FABER

-FOLK

FOLKS

1

2

3

4

5

6

A list of potential separators

DUTU

DVXGHSJF

DZ

E

EBQX

ELEEMOSYNARY

CAMP

-DUTTON

EMBRY

-EVANS

SNU-OOPSLA Lab.

10.5 The Simple Prefix B+ Tree

• Index like B-tree + blocks of sequential sets

• The use of simple prefixes

• prefixes of the keys rather than actual keys

• contains shortest separators

• N separators -> N+1 children

• Properties of B+ tree

• B-tree like Index

• Sequential data set

• Indexed-sequential file

SNU-OOPSLA Lab.

Index

set

BO

CAM

F

FOLKS

-BERNE

BOLEN

-CAGE

CAMP

-DUTTON

EMBRY

-EVANS

FABER

-FOLK

FOLKS

1

2

3

4

5

6

A B-tree index set for the sequence set,

forming a simple prefix B+ tree

SNU-OOPSLA Lab.

10.6 Simple Prefix B+ Tree Maintenance (1)

• Changes localized to single blocks in the sequence set

• deletion without concatenation, redistribution

• e.g. delete EMBRY, FOLKS

• insertion without splitting

• e.g. insert EATON

SNU-OOPSLA Lab.

from the sequence set

E

BO

CAM

F

FOLKS

-BERNE

BOLEN

-CAGE

CAMP

-DUTTON

ERVIN

-EVANS

FABER

-FOLK

FROST

1

2

3

4

5

6

SNU-OOPSLA Lab.

10.6 Simple Prefix B+ Tree Maintenance(2)

• Changes involving multiple blocks in the sequence set

• split, concatenation : propagate to index set

• change the number of blocks in the sequence set

• change the number of separators

• change the index set

• insertion with splitting

• e.g. overflow in block1

• block1, block7 with separator AY

• deletion with concatenation/redistribution

• e.g. underflow in block2 block2, block3

split

concatenation

SNU-OOPSLA Lab.

the consequent addition of block 7

BO

E

AY

CAM

F

FOLKS

-AVERY

AYERS

-BERNE

BOLEN

-CAGE

CAMP

-DUTTON

ERVIN

-EVANS

FABER

-FOLK

FROST

1

7

2

3

4

5

6

SNU-OOPSLA Lab.

the consequent concatenation of blocks 2 and 3

E

AY

BO

F

FOLKS

-AVERY

AYERS

-BERNE

BOLEN

-DUTTON

ERVIN

-EVANS

FABER

-FOLK

FROST

1

7

2

4

5

6

SNU-OOPSLA Lab.

** insert/delete in the sequence set as if there is no B-tree index set

if blocks are split

a new separator must be inserted into the index set

if blocks are concatenated

a separator must be removed from the index set

if records are redistributed between blocks

the value of a separator in the index set must be changed

else

no propagation to index set

SNU-OOPSLA Lab.

• size of an index node for the index set

• == size of a data block in the sequence set

• Reasons for using a common block size

• the best size for sequence set is usually the best for the index set

• a common block size makes it easier to implement a buffering scheme

• the index set blocks and sequence set blocks are often mingled within the same file

• to avoid seeking between separate files while accessing the simple prefix B+ tree

SNU-OOPSLA Lab.

10.8 Internal Structure of Index Set Blocks: A variable-order B-tree

• Variable-length shortest separator

• possibility of packing them into a node

• separator index (fixed length) : means of performing binary searches on a list of variable-length entities

• A simple prefix B+ tree with a variable order

• not maximum order -> not minimum depth

• decisions about when to split, concatenate, or redistribute become more complicated

SNU-OOPSLA Lab.

As, Ba, Bro, C, Ch, Cra, Dele, Edi, Err, Fa, File

00 02 04 07 08 10 13 17 20 23 25

Variable-length separators and corresponding index

Separator count

Total length of separators

11

28

00 02 04 07 08 10 13 17 20 23 25

B00 B01 ..... B10 B11

Relative block

numbers

Separators

Index to separators

Structure of an index set block

SNU-OOPSLA Lab.

• One way is successive insertions and splits

• working from a sorted file and then

• place the records into sequence set block

• if one block is full

• determine the separator and insert it into the index set block

• place the records into new sequence set block

SNU-OOPSLA Lab.

• the output can be written sequentially

• simple than succcessive insert & split

• can load 100% utilization (c.f. insert & split produces blocks between 67~80% full)

• creating a degree of spatial locality

SNU-OOPSLA Lab.

10.10 B+ Trees

• Contains copies of actual keys

• cf. simple prefix B+ tree : separator

ALWAYS/ASPECT/BETTER

00

06

12

Next separator: CATCH

Next sequence

set block:

ACCESS

-ALSO

ALWAYS

ASPECT

-BEST

BETTER

-CAST

CATCH

-CHECK

SNU-OOPSLA Lab.

10.11 B-Tree, B+ Tree and Simple Prefix B+Tree in Perspective

• Shared characteristics

• Paged index structures : broad and shallow

• Height-balanced

• Growing from bottom-up

• Possible to obtain greater storage efficiency through two-three block splitting, concatenation, redistribution

• Can be implemented as virtual tree structures

• Can be adapted for variable-length records

SNU-OOPSLA Lab.

• General Characteristics

• Information can be found at any level of the B-tree

• B-tree take up less space than Ｂ+ tree (Ｂ+ tree 　ｈas additional space)

• Ordered sequential access

• Through in-order traversal of the tree(virtual tree is necessary)

• Separated record files(B-tree has only pointers) are not workable

SNU-OOPSLA Lab.

B＋Trees

• General Characteristics

• Separation of index set and sequence set

• Separators : copies of keys

• Shallower tree than B-tree

• Ordered sequential access

• Sequence set is truly linear

SNU-OOPSLA Lab.

Simple Prefix B+ Trees

• General Characteristics

• Separators : smaller than actual keys

• Shallower than Ｂ+ Trees

• Separator compression, variable-length field management overhead

• Ordered sequential access

• Sequence set is truly linear (same as Ｂ+ Tree)

SNU-OOPSLA Lab.

• 10.1 Indexed Sequential Access

• 10.2 Maintaining a Sequence Set

• 10.3 Adding a Simple Index to the Sequence Set

• 10.5 The Contents of the Index: Separators Instead of Keys

• 10.6 The Simple Prefix B+ Tree Maintenance

• 10.7 Index Set Block size

• 10.8 Internal Structure of the Index Set Blocks: A variable-order B-Tree