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Chapter 12: Indexing and Chapter 12: Indexing and HashingHashing

IndexingIndexing Basic ConceptsBasic Concepts Ordered Indices Ordered Indices B+-Tree Index FilesB+-Tree Index Files

HashingHashing StaticStatic Dynamic HashingDynamic Hashing

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Basic ConceptsBasic Concepts

ValueValue

Search KeySearch Key - set of attributes used to - set of attributes used to look up records in a file.look up records in a file.

value

record

search key pointer

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Index Evaluation MetricsIndex Evaluation Metrics

Access types supported efficiently. E.g., Access types supported efficiently. E.g., Point query: find “Tom”Point query: find “Tom” Range query: find students whose age is Range query: find students whose age is

between 20-40between 20-40 Access timeAccess time Update timeUpdate time Space overheadSpace overhead

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Ordered IndicesOrdered Indices In an In an ordered indexordered index, , index entries are index entries are

stored sorted on the search key value. stored sorted on the search key value. E.g., author catalog in library.E.g., author catalog in library.

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2010

4030

6050

8070

10090

10305070

90110130150

170190210230

Primary index

Also called clustering index

•The search key of a primary index is usually but not necessarily the primary key.

same order

Search key

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Search key

5030

7020

4080

10100

6090

10203040

506070...

Secondary index: non-clustering index.

different order

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Sequential File

2010

4030

6050

8070

10090

Dense Index

10203040

50607080

90100110120

Dense Index: contains index records for every search-key values.

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Sequential File

2010

4030

6050

8070

10090

Sparse Index

10305070

90110130150

170190210230

Sparse Index: contains index records for only some search-key values.

Applicable when records are sequentially ordered on search-key

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Secondary indexesSecondary indexes Sequencefield

5030

7020

4080

10100

6090

• Sparse index

302080

100

90...

does not make sense!

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Sequential File

2010

4030

6050

8070

10090

Sparse 2nd level

10305070

90110130150

170190210230

1090

170250

330410490570

Multilevel IndexMultilevel Index

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Secondary indexesSecondary indexes Sequencefield

5030

7020

4080

10100

6090

10203040

506070...

105090...

sparsehighlevel

Lowest level is denseLowest level is dense Other levels are sparseOther levels are sparse

Multilevel IndexMultilevel Index

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Conventional indexesConventional indexes

Advantage:Advantage:

- Simple- Simple- Index is sequential file good - Index is sequential file good

for for scansscansDisadvantage:Disadvantage:

- Inserts expensive- Inserts expensive

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OutlineOutline

Conventional indexesConventional indexes B+-Tree B+-Tree NEXT NEXT

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NEXT: Another type of indexNEXT: Another type of index Give up on sequentiality of indexGive up on sequentiality of index Try to get “balance”Try to get “balance”

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RootRoot

B+Tree Example n=4

100

120

150

180

30

3 5 11

30

35

100

101

110

120

130

150

156

179

180

200

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Sample non-leafSample non-leaf

57

81

95

Key is moved (not copied) from lower level non-leaf node to upper level non-leaf node

to keys to keys to keys to keys

< 57 57 k<81 81k<95 95

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Sample leaf node:Sample leaf node:

From non-leaf nodeFrom non-leaf node

to next leafto next leaf

in sequencein sequence

57

81

95

To r

eco

rd

wit

h k

ey 5

7

To r

eco

rd

wit

h k

ey 8

1

To r

eco

rd

wit

h k

ey 8

5

Key is copied (not moved) from leaf node to non-leaf node

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n=4n=4

Leaf:Leaf:

Non-leaf:Non-leaf:

30

35

30

30 35

30

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Size of nodes: Size of nodes:

n pointersn pointers

n-1 keysn-1 keys

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Don’t want nodes to be too Don’t want nodes to be too emptyempty

Use at leastUse at least

Root : 2 pointersRoot : 2 pointers

Non-leaf: Non-leaf: n/2n/2 pointers pointers

Leaf : Leaf : (n-1)/2(n-1)/2 keys keys

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Full nodeFull node min. nodemin. node

Non-leafNon-leaf

LeafLeaf

n=4

12

01

50

18

0

30

3 5 11

30

35

counts

even if

null

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B+tree rulesB+tree rulestree of order tree of order nn

(1) All leaves at same lowest level(1) All leaves at same lowest level(balanced tree)(balanced tree)

(2) Pointers in leaves point to records(2) Pointers in leaves point to records except for “sequence pointer”except for “sequence pointer”

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(3) Number of pointers/keys for B+tree(3) Number of pointers/keys for B+tree

Non-leaf(non-root) n n-1 n/2 n/2- 1

Leaf(non-root) n n-1

Root n n-1 2 1

Max Max Min Min ptrs keys ptrsdata keys

(n-1)/2 (n-1)/2

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Insert into B+treeInsert into B+tree

(a) simple case(a) simple case space available in leafspace available in leaf

(b) leaf overflow(b) leaf overflow

(c) non-leaf overflow(c) non-leaf overflow

(d) new root(d) new root

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(a) Insert key = 32(a) Insert key = 32 n=43 5 11

30

31

30

100

32

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(b) Insert key = 7(b) Insert key = 7 n=4

3 5 11

30

31

30

100

3 5

7

7

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(c) Insert key = 160(c) Insert key = 160 n=4

10

0

120

150

180

150

156

179

180

200

160

18

0

160

179

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(d) New root, insert 45(d) New root, insert 45 n=4

10

20

30

1 2 3 10

12

20

25

30

32

40

40

45

40

30new root

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(a) Simple case - (a) Simple case - no exampleno example

(b) Coalesce with neighbor (b) Coalesce with neighbor (sibling)(sibling)

(c) Re-distribute keys(c) Re-distribute keys

(d) Cases (b) or (c) at non-leaf(d) Cases (b) or (c) at non-leaf

Deletion from B+treeDeletion from B+tree

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(b) Coalesce with sibling(b) Coalesce with sibling Delete 50Delete 50

10

40

100

10

20

30

40

50

n=5

40

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(c) Redistribute keys(c) Redistribute keys Delete 50Delete 50

10

40

100

10

20

30

35

40

50

n=5

35

35

32

40

45

30

37

25

26

20

22

10

141 3

10

20

30

40

(d) Non-leaf coalese(d) Non-leaf coalese Delete 37Delete 37

n=5

40

30

25

25

new root

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B+tree deletions in B+tree deletions in practicepractice

– Often, coalescing is Often, coalescing is notnot implemented implemented Too hard and not worth it!Too hard and not worth it!

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Index Definition in SQLIndex Definition in SQL

Create an indexCreate an indexcreate indexcreate index <index-name> <index-name>

onon <relation-name> (<attribute-list>) <relation-name> (<attribute-list>)

E.g.: create index gindex on country(gdp);E.g.: create index gindex on country(gdp);

To drop an index To drop an index drop index drop index <index-name><index-name>

E.g.: drop index gindex;E.g.: drop index gindex;