Dual Bitmap Index: Space-Time Efficient Bitmap Index for Equality and Membership Queries

Dual Bitmap Index: Space-Time Efficient Bitmap

Index for Equality and Membership Queries

Niwan Wattanakitrungroj and Sirirut Vanichayobon

Information Systems Technology and Applied Research LaboratoryDepartment of Computer Science, Prince of Songkla University

Information Systems Technology and Applied Research 2/24

Introduction

Variations of Bitmap Index

- Simple Bitmap Index

- Interval Bitmap Index

- Scatter Bitmap Index

- Encoded Bitmap Index

- Dual Bitmap Index

Performance Study

Conclusion

Outline


2541

SO N G K L A

B K K

D ata M art

D ata W ar ehouse0

10

20

30

40

50

60

70

80

90

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1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

East

West

North

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

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Introduction

- A data warehouse is a large repository of information accessed through OLAP application.

- A majority of requests for information from a data warehouse involve dynamic ad hoc queries.

- The ability to answer these queries quickly is a critical issue in the data warehouse environment.


Introduction

Summary tables

Indexes

Parallel machines

To speed up query processing :


Bitmap Index

simple to represent

uses less space

more CPU-efficient

low-cost Boolean operations

Characteristic :

Introduction :


Bitmap IndexName Gender Education

Suda F BS

Wichai M BS

Jonh M MS

Marry F PhD

Somsak M BS

… …

F

1

0

0

1

0

…

BS

1

1

0

0

1

…

MS

0

0

1

0

0

…

M

0

1

1

0

1

…

PhD

0

0

0

1

0

…

RID

1

2

3

4

5

…

RID

1

2

3

4

5

…

Select Count(*)

From Employee

Where Gender=“F”;

Answer : 2

Select Name

From Employee

Where Gender=“M” and

Education=“MS”

Answer : John

Introduction :

Select Name

From Employee

Where Education in {MS,PhD}

Answer : John, Marry

Employee Table

Equality Query

Membership Query


Introduction






- Dual Bitmap Index

Performance Study

Conclusion

Outline


Related WorkSimple Bitmap Index C = 15 15 bitmap vectors


Let C be a number of distinct values of the indexed attribute(Cardinallity).

Bitmap vectors : 0 1 2 1, , ,..., CS S S S " " vA v s

Query :

" " 22A S


3v

Interval Bitmap Index Related Work

C = 15 8 bitmap vectors


Bitmap vectors : 1

0 1 2 2, , ,..., , C

I I I I

0

0

1

1

0

if 0, 0,

if 1, 2,

if 1, 3,

" " if ,

v v

v

I v m

I v C

I v C

A v I I v m

I I

12

1

0

if , 0,

if m 1, 0,

( ) if 1

C

v m v m

v m m

I I v C m

I I v C Query , jI j j m1,

2 C

m" " 2 32A I I


Scatter Bitmap Index C = 15 8 bitmap vectors,


Related Work

Bitmap vectors : 1 2 1 0 1, ,..., , , ,...,C CL L L Z Z Z

1, m C

( - ) ( )

( - ) mod( )

if " "

otherwise

1 1 1

1 1 1

0v m v m

v m v m

Z Z vA v

Z L

m = 5

Query

" " 1 22A Z L


Encoded Bitmap Index Related Work

C = 15 4 bitmap vectors


Mapping all Bitmap Vector

Query :Bitmap vectors : log 10 1 2, , ,..., CE E E E

" "2A


Introduction






- Dual Bitmap Index

Performance Study

Conclusion

OutlineVariations of Bitmap Index


Dual Bitmap Index


Encoding Scheme of five bitmap indices

Need

C bitmap vectors

Need

bitmap vectors

2

CNeed

bitmap vectors

2 C

Need

bitmap vectors

log C Need

bitmap vectors

. . 2 0 25 0 5C


Dual Bitmap Index



1. Assign an increasing sequence of numbers to each of the distinct values of A (i.e., 0,1,…,C-1).

4. For each value v on record at position i in A

1

0

iD

if i = r and s

otherwise

where 2( ) 0.25 0.5 ,r hiC v

rrnrn

vrs mod2

)1)((1

and v is the value of an indexed attribute for any record.

Creation of Dual Bitmap Index

C =15 A = {0,1,2,…,14}


2. Calculate n :

2 0.25 0.5n C (The total number of bitmap vectors created )

hiC

2

nhiC3. Calculate : (the highest value of C that can be represent

by n bitmap vector)

n = 6

hiC = 15


1. Find the sequence number of the searching value.

2. " " r sA v D D

where 2( ) 0.25 0.5 ,r hiC v

rrnrn

vrs mod2

)1)((1

and v is the value of an indexed attribute for any record.

Equality and Membership Queries

“A = 2” 5 2D D

Variations of Bitmap Index : Propose Bitmap Index


Introduction






- Dual Bitmap Index

Performance Study

Conclusion

Outline


Performance study


Performance study

Number of bitmap vectors used to represent an attribute with cardinality C

(Space)

Scatter

Dual

Encoded

Simple

Interval

Scatter

Dual

Encoded


Performance study


Space-Time Trade-off for five Bitmap IndicesSpace-Time Trade-off for five Bitmap Indices

C=50, N=1,000,000 (The data sets from TPC-H Benchmark)

Performance study

Simple

Interval

Scatter

Encoded

Dual


Introduction






- Dual Bitmap Index

Performance Study

Conclusion

Outline


Conclusion

Dual bitmap index uses less space while maintaining query processing time for equality and membership queries.

Dual Bitmap Index achieves this by representing each attribute value using only two bitmap vectors, and only the low-cost Boolean AND operation is used to answer equality query.

Dual Bitmap Index has better space-time performance than the other bitmap indexing techniques.

Simple Bitmap Index requires the most space.

Encoded Bitmap Index’ s processing time is the worst.


Thank You

Question & answer

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Dual Bitmap Index: Space-Time Efficient Bitmap Index for Equality and Membership Queries