hashing tuto

8/10/2019 Hashing Tuto

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DYNAMIC HASHING

TECHNIQUES

Presented By:Anila Sahar Butt

MSIT-8



EXTENSIBLE HASHING



Advance Databases Concepts 3

Extensible Hashing

Use i of b bits output by hash functionb

h(K)

usei grows over time….

00110101



Advance Databases Concepts 4

Use directory

h(K)[i ] to bucket...

.

.

.



Example

• h(k) is 4 bits• 2 keys/bucket

0

1

10001

1

1001

1100

1



Example

• Insert

0

1

10001

1

1001

1010 1

1100

11001010

00

01

10

11

2

2

21



LINEAR HASHING



Linear Hashing• Family of Hash Functions

– h0, h1, h2, …..

•

During each round only two hash functions are used – At level (round number)• hLevel• hLevel + 1

• Hash Function• h i(value) = h(value) mod (2 iN)• N is “Initial Number of buckets” • i is level (Round number), initialize to 0



Linear Hashing

• Next Pointer point the bucket that is to split

• At any given point within the round we have – Buckets that have been split – Buckets that are yet to split – Buckets created by splits in this round

• If Next bucket is split at any Level, Hash function h Level + 1 redistributes entries between this bucket and its split image



Example

Level = 0 , N = 4

h1 h0 Primary PagesNext=0

000 00

001 01

010 10

011 11

32 44 36

9 25 5

14 18 10 30

31 35 7 11



SIMPLE INSERTION

• Insert 37 – Apply hash Function h0

37mod (2 i N) = 37 mod 4 = 1 (01)

h1 h0 Primary PagesNext=0

000 00

001 01

010 10

011 11

32 44 36

9 25 5

14 18 10 30

31 35 7 11

37



Over Flow• Insert 43

– Apply hash Function h043 mod (2 i N) = 43 mod 4 = 3 (11)

– Check bucket (11) capacity• Full Add Over Flow Page , insert value in it

– If Over Flow• Split Bucket pointed by Next Pointer• Add split image at the end of buckets• Redistribute the values of split bucket• Move Next Pointer to Next Bucket



Over Flow

Level = 0 , N = 4

h1 h0 Primary Pages Overflow Pages

Next=0 000 00

Next=1

001 01

010 10

011 11

100 00

9 25 5

14 18 10 30

31 35 7 11

32 44 36

44 36

43

32



Example

By Inserting 22, 66, 34

Level = 0 , N = 4


000 00

001 01

010 10 Next=3

011 11

100 00

101 01

110 10

9 25

66 18 10 34

31 35 7 11 43

32

44 36

5 37 29

14 30 22



Insertion in Split Bucket• Insert 13

– Apply hash Function h013 mod (2 i N) = 13 mod 4 = 1 (01)

– Check bucket (01) capacity, and bucket category• Bucket above next pointer Means?• Check newly inserted value proper place by applying second hash

function

– 13 mod (2 i N) = 13 mod 8 = 5 (101)

– Insert new value in Split Image



Example

By Inserting 13

Level = 0 , N = 4


000 00

001 01

010 10 Next=3

011 11

100 00

101 01

110 10

9 25

66 18 10 34

31 35 7 11 43

32

44 36

5 37 29

14 30 22

13



Splitting Last Bucket of a Round(Level)

• Insert 50 – Apply hash Function h0

50 mod (2 i N) = 50 mod 4 = 2 (10)

– Apply hash Function h1

50 mod (2 i N) = 50 mod 8 = 2 (010)

– Check bucket (10) capacity• Full Add Over Flow Page , insert value in it

–

If Over Flow• Split Bucket pointed by Next Pointer• Add split image at the end of buckets• Redistribute the values of split bucket• As Round is complete now. Move Next to the start of File. Increment Level to 1



Example

Insert 50Level = , N = 4

Primary Pages Overflow Pages

9 25

66 18 10 34

43

32

44 36

5 37 29

14 30 22

50

31 35 7 1143 35 11

31 7

Next=3

Next=0

01

h1

000

001

010

011

100

101

110

111

h0

00

01

10

11

00

01

10

11



THANKS



QUIZ



Q1- Insert 51



Q2- Insert 15

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