tree structured indexing

8/6/2019 Tree Structured Indexing

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TREE STRUCTUREDINDEXING

Dr. Hari Om Gupta

Professor, Department of Electrical Engineering

IIT Roorkee


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Indexed Sequential Access Method (ISAM)

P0 K 1 P1 K 2 P2 K m Pm

Format for an Index Page or Block


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K 1 K 2 K n

Page 1 Page 2Page n+1

Page 3

One level index structure

Index file

Data file


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ISAM INDEX STRUCTURE

- - -

- - - - - -

- - - - - - - -

OVER FLOWPAGES

PRIMARY PAGES

NON LEAF PAGES

LEAFPAGES


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Non leaf pages contains index entries of the form(search key value,page id )

Can use alternative (1) or (2) or (3), but commonly alternate (2) or (3)is used. (key, r id)

Data pages

Index pages

Overflow pages

Page allocation in ISAM


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18 33

42

51 64

20* 27* 33* 37* 42* 46* 64* 97*10* 15* 51* 55*

Root

Sample ISAM Tree


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18 33

42

51 64

20* 27* 33* 37* 42* 46* 64* 97*10* 15* 51* 55*

Root

Sample ISAM Tree23* 52* 63*

53*

Non leaf pages

Leaf pages

Overflow pages

ISAM Tree after inserts


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To search a record , the number of disk I/O is equal to the number of levels of the tree and is equal to

log F N N= no. of primary leaf pages; F= Fan-out

1,000,000 records file, 10records/page and F=100 N=1,000,000/10= 100,000

Levels=log 100(100,000)=3Thus number I/O of the tree= 3 to reach the required page

If we use binary search for the sorted file, number of stepsEqual to

log 2(100,000)= 17 steps

Deletion in ISAM: BLANK OVERFLOW PAGES ARE

RELEASED WHEREAS BLANK PRIMARY PAGES ARERETAINED.


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18 33

42

51 64

20* 27* 42* 46* 64* 97*10* 15* 51* 55*

Root

Sample ISAM Tree23* 52* 63*

Non leaf pages

Leaf pages

Overflow pages

ISAM Tree after deletes (53,33,37)


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Disadvantages

Long overflow chains Retrieval time increases

to overcome this

(a) Initially 20% of each page is kept free.

(b) Eliminate overflow chains by a complete reorganization

of the file.

There may be to many blanks if data shrink

Advantages No need to lock index level pages thus queues & waiting

time to get access to a page is reduced in comparison to B + tree.

It is static , response time will be less if overflow pages and blank pages are few .


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B+ TREE(A DYNAMIC INDEX STRUCTURE)

Operations (insert, delete) on tree keep it balanced.A minimum occupancy of 50% is guaranteed for each node exceptroot node.

Searching for a record requires just a traversal from the root node

to the appropriate leaf.Leaf pages are sorted and have pointers to link from one page toother page.Height is normally 3 or 4.Index level pages are to be locked tree dynamically changes.


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K 1 K 2 K n

Page 1 Page 2Page n+1

Page 3


Index file

Data file


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Page 1 Page 2Page n

Page 3


Index entries

Data entries

Non leaf nodes

Leaf pages (a sequence set-> sorted file)

B+ tree structure : index file


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B+ Tree

A node other then root node may contain m entries such thatd


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Insert

14 17 24 30

1 3 5 7 15 16 19 20 23 24 26 29 33 34 39 41

B+ tree, order d=2Insert record with key value 8

1 3 5 7 8

5

Root

Split leaf pages during insert of entry 8

Left side Right sided d+1


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5 13

1 3 15 16 19 20 23 24 26 29 33 34

After inserting record with key value 8

5 7 8

24 30

17Root


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Insert8 17 24 30

1 3 5 7 8 15 16 19 20 23 24 26 29 33 34 39 41

B+ tree after inserting Entry 8 using redistribution

Root

F or Redistribution

Have to retrieve the sibling with empty cell

Checking for redistribution increases I/O for index node spit.Thus spit may not be advantageous.

F or growing files

(a) Do not redistribute for non leaf vacancies

(b) Limited redistribution ( Only with neighbours ) for leaf pages


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DeleteSearch & delete with following restriction

If a node is at minimum occupancy before deletion anddeletion causes it to go below the occupancy threshold. Whenthis happens, we must either redistribute entries from anadjacent sibling, or merge the node with a sibling, in order tomaintain minimum occupancy


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5 13

1 3 15 16 19 20 24 26 29 33 34

After deleting record with key value 23

5 7 8

24 30

17Root

19 24 26 29 33 34 39 41

24 30

19 24 26 29 33 34 39 41

30

Partial B+ Tree during deletion of Entry 20


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5 13 17 30

1 3 5 7 8 15 16 19 24 26 29 33 34 39 41

Root

B+ Tree during deletion of Entry 20


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DuplicatesISAM

Overflow pagesB+ Tree

Use (key, r id) the record entry no. along with keymay be used as search key


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B+

Tree in PracticeK ey Compression and Code

F an out of the tree= F

Height of the tree = log F (# of data entry)Thus higher the fan-out, lower is tree height andresponse time will be less

To increase the fan out, use small size of search key.Code is normally used to reduce the size of the searchkey.


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Dani LalMan

Data RamVerma

Devand Sagar

Dani LalMan

Dara Singh . . .

Dan Data DevAfter key compression


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B+ Tree Bulk Loading

1 5 6 8 9 10 12 14 15 16 20 22 31 35 39 41

RootSorted pages of data entries not yet in B+tree

1 5 6 8 9 10 12 14 15 16 20 22 31 35 39 41

6 9

RootSorted pages of data entries not yet in B+tree


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1 5 6 8 9 10 12 14 15 16 20 22 31 35 39 41

6

RootSorted pages of data entries not yet in B+tree12

9

1 5 6 8 9 10 12 14 15 16 20 22 31 35 39 41

6

Root

data entries not yet in B+tree

12

9 15

20 31


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1 5 6 8 9 10 12 14 15 16 20 22 31 35 39 41

6

Root

12

9

20 39

31

15

Complete B+

Tree


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tree structured indexing

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