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OLAP (Online Analytical Processing): Iterative Data Cubes Excerpt - - PowerPoint PPT Presentation

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OLAP (Online Analytical Processing): Iterative Data Cubes Excerpt from Presentation by M. Riedewald 1 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani Content Introduction to Multidimensional Databases (from A.R. 20 and 21)

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SLIDE 1

1 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

OLAP (Online Analytical Processing): Iterative Data Cubes

Excerpt from Presentation by M. Riedewald

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SLIDE 2

2 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Content

Introduction to Multidimensional Databases

(from A.R. 20 and 21)

Focus Application: OLAP

Prefix-Sum Data Cube (from A.R. 16) Dynamic Data Cube (from A.R. 17) Iterative Data Cube (from A.R. 18) Wavelet-based approaches

  • Compact Data Cube (from A.R. 19)
  • ProPolyne (from A.R. 22 and 23)
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SLIDE 3

3 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Flexible Data Cubes for Online Aggregation

Mirek Riedewald, Divyakant Agrawal, and Arm El Abbadi

Iterative Data Cube

Space-Efficient Data Cubes for Dynamic Environments

Mirek Riedewald, Divyakant Agrawal, Arm El Abbadi, and Renato Pajarola

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SLIDE 4

4 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Outline

What is IDC? Pre-Aggregation Techniques Querying and Updating an IDC Selecting an IDC IDC with more than One Dimension Conclusion

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SLIDE 5

5 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Iterative Data Cube (IDC)

Provides a modular framework for combining one-

dimensional aggregation techniques to create space-

  • ptimal high-dimensional data cubes.

For each dimension a different one-dimensional technique can be

selected.

Combining the one-dimensional techniques is easy.

Allows a variety of cost tradeoffs between query and

update.

Generalizes some of the pre-aggregation approaches:

PS (Prefix Sum) SRPS (Space-Efficient Relative Prefix Sum) SDDC (Space-Efficient Dynamic Data Cube)

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SLIDE 6

6 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Prefix Sum (review)

3 3 6 4 2 2 1 5 3

Original array PS array

…………

29 26 23 17 13 11 9 8 3

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SLIDE 7

7 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Relative Prefix Sum

The data cube is partitioned into a set of disjoint

hyper-rectangles of equal size (termed boxes)

Any cell in box B stores the value:

SUM(A[l1, l2, …, ld]:A[c]) where for all i: 1 <= i <= d li=0 , if ci=ai li=ai+1 , if ai+1 <= ci < ai+k

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SLIDE 8

8 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

5 6

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1

SRPS array (block size 3)

8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 9

9 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 3 7 9 2 5 1 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 10

10 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 3 11 7 9 2 5 1 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 11

11 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 3 11 7 9 2 18 5 1 11 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 12

12 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 14 15 3 11 7 9 2 18 5 1 11 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 13

13 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 14 15 3 29 11 7 9 2 18 5 1 11 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 14

14 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 20 14 15 3 29 11 7 9 2 18 5 1 11 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 15

15 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 51 20 14 15 3 29 11 7 9 2 18 5 1 11 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 16

16 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 19 10 42 9 6 23 13 8 7 8 4 23 4 10 6 7 47 23

182

61 21 93 36 24 25 6 6 2 52 16 4 24 9 5 6 5 4 24 7 10 3 4 34 18 99 35 16 51 20 14 15 3 18 7 55 21 11 29 11 7 9 2 6 34 15 18 5 1 6 23 6 11 6 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 17

17 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 19 10 42 9 6 23 13 8 7 8 4 1 23 4 3 10 6 4 2 7 47 23

182

61 21 93 36 24 25 6 6 2 52 16 4 24 9 5 6 5 4 1 24 7 3 10 3 2 4 4 34 18 99 35 16 51 20 14 15 3 18 7 55 21 11 29 11 7 9 2 6 2 34 15 8 18 5 3 7 1 6 3 23 6 2 11 6 5 3 8 7 6 5 4 3 2 1

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 18

18 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1

Original array SRPS array (block size 3) Partition into blocks of equal size

6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2 4 4 2 8 2 5 3 5 1 2 3 3 7 5 4 3 3 3 2 4 2 2 4 2 1 7 8 6 2 3 7 1 3 3 6 4 2 2 1 5 3 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1

Inner cells Border cells Border cells include cells from outside the block into their aggregation. Inner cells store sums local to the block.

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 19

19 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

3 3 6 4 2 2 1 5 3

Original array SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 20

20 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

6 6 6 3 3 6 4 2 2 1 5 3

Original array SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 21

21 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

3 3 6 4 2 2 1 5 3

Original array

6 6 11 6

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 22

22 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

3 3 6 4 2 2 1 5 3

Original array

6 23 6 11 6

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 23

23 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

3 3 6 4 2 2 1 5 3

Original array

6 3 23 6 2 11 6 5 3

SRPS array (block size 3)

Space-Efficient Relative Prefix Sum (cont’d)

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SLIDE 24

24 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Partition to boxes the same as SRPS except for the

following:

  • 1. The side-length of a box is set to k=n/ 2 (i.e., the cube is

partitioned into 2d equi-size boxes)

  • 2. Aggregation of the border cells remain the same as SRPS,

but not for inner cells:

  • The region that contains the inner cells is recursively partitioned into

2d boxes until there is no inner cells!

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SLIDE 25

25 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

2 5 1 3 1 2 4 2 1 6 9 5 6 9 1 2 3 1 3 4 5 8 3 3 1 9 1 3 2 2 4 2 7 1 4 3 3 9 1 7 2 5 4 6 2 1 1 5 8 1 6 3 3 2 5 2 3 1 7 4 3 3 1 2 4 4 1 2 8 2 5 3 5 1 2 3 3 4 7 5 4 3 3 3 2 4 2 2 2 4 2 1 7 8 6 2 3 7 1 1 3 3 6 4 2 2 1 5 3 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1

Partition into 2d blocks of equal size d:Dimensionality

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SLIDE 26

26 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

2 5 1 3 1 2 4 2 1 6 9 5 6 9 1 2 3 1 3 4 5 8 3 3 1 9 1 3 2 2 4 2 7 1 4 3 3 9 1 7 2 5 4 6 2 1 1 5 8 1 6 3 3 2 5 2 3 1 7 4 3 3 1 2 4 4 1 2 8 2 5 3 5 1 2 3 3 4 7 5 4 3 3 3 2 4 2 2 2 4 2 1 7 8 6 2 3 7 1 1 3 3 6 4 2 2 1 5 3 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1

Partition into 2d blocks of equal size d:Dimensionality

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SLIDE 27

27 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

2 5 1 3 1 2 4 2 1 6 9 5 6 9 1 2 3 1 3 4 5 8 3 3 1 9 1 3 2 2 4 2 7 1 4 3 3 9 1 7 2 5 4 6 2 1 1 5 8 1 6 3 3 2 5 2 3 1 7 4 3 3 1 2 4 4 1 2 8 2 5 3 5 1 2 3 3 4 7 5 4 3 3 3 2 4 2 2 2 4 2 1 7 8 6 2 3 7 1 1 3 3 6 4 2 2 1 5 3 9 8 7 6 5 4 3 2 1 76 17 9 60 11 8 42 6 7 28 4 6 77 65 45 25

126

74 54 29 19 18 5 86 16 4 69 12 3 50 9 2 33 7 1 13 12 9 6 17 10 8 6 5 3 9 8 7 6 5 4 3 2 1

Processing for row using SRPS Processing for column using SRPS

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SLIDE 28

28 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

2 5 1 3 1 2 4 2 1 6 9 5 6 9 1 2 3 1 3 4 5 8 3 3 1 9 1 3 2 2 4 2 7 1 4 3 3 9 1 7 2 5 4 6 2 1 1 5 8 1 6 3 3 2 5 2 3 1 7 4 3 3 1 2 4 4 1 2 8 2 5 3 5 1 2 3 3 4 7 5 4 3 3 3 2 4 2 2 2 4 2 1 7 8 6 2 3 7 1 1 3 3 6 4 2 2 1 5 3 9 8 7 6 5 4 3 2 1 9 3 76 7 1 17 9 9 39 9 13 60 7 30 7 13 11 8 13 9 42 8 4 6 7 1 10 3 3 28 1 14 2 5 4 6 77 65 45 25

126

74 54 29 19 18 5 11 7 86 6 2 16 4 7 35 15 7 69 14 28 5 9 12 3 16 4 50 9 4 9 2 2 7 2 1 33 8 11 2 3 7 1 13 12 9 6 17 10 8 6 5 3 9 8 7 6 5 4 3 2 1

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SLIDE 29

29 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

2 5 1 3 1 2 4 2 1 6 9 5 6 9 1 2 3 1 3 4 5 8 3 3 1 9 1 3 2 2 4 2 7 1 4 3 3 9 1 7 2 5 4 6 2 1 1 5 8 1 6 3 3 2 5 2 3 1 7 4 3 3 1 2 4 4 1 2 8 2 5 3 5 1 2 3 3 4 7 5 4 3 3 3 2 4 2 2 2 4 2 1 7 8 6 2 3 7 1 1 3 3 6 4 2 2 1 5 3 9 8 7 6 5 4 3 2 1 2 9 1 3 76 2 7 2 1 17 9 9 39 9 13 60 7 30 7 13 11 8 3 13 1 9 42 3 8 2 4 6 7 1 10 3 3 28 1 14 2 5 4 6 77 65 45 25

126

74 54 29 19 18 5 2 11 1 7 86 3 6 1 2 16 4 7 35 15 7 69 14 28 5 9 12 3 4 16 5 4 50 3 9 2 4 9 2 2 7 2 1 33 8 11 2 3 7 1 13 12 9 6 17 10 8 6 5 3 9 8 7 6 5 4 3 2 1

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SLIDE 30

30 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

1 3 3 6 4 2 2 1 5 3

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SLIDE 31

31 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

1 3 3 6 4 2 2 1 5 3 17

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SLIDE 32

32 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

1 3 3 6 4 2 2 1 5 3 12 17 8

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SLIDE 33

33 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Space-Efficient Dynamic Data Cube

Original array SDDC array

1 3 3 6 4 2 2 1 5 3 1 12 3 6 17 2 8 1 5 3

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SLIDE 34

34 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008 2 29 26 23 17 13

3

30 27 24 18 14

3 3 6 4 2 1 5 3

11 9 8 3

Query and Update Comparison (PS)

Original array A

3 3 6 4 2 2 1 5 3

Query: 1+ 2+ 2+ 4= 9 cost: 4 Update: A[4]= 3 cost: 1 PS Array

29 26 23 17 13 11 9 8 3

Query: 17-8= 9 cost: 2 Update: A[4]= 3 cost: 5

3 3 6

4 2 2 1

5 3

29 26 23 17 13 11 9 8 3

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SLIDE 35

35 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array A

3 3 6 4 2 2 1 5 3 3 3 6 4

3

2 1 5 3

Query: 1+ 2+ 2+ 4= 9 cost: 4 Update: A[4]= 3 cost: 1 SRPS Array (block size 3)

6 3 23 6 2 11 6 5 3 6 3 24 7 3 11 6 5 3

Query: 11+ 6-3-5= 9 cost: 4 Update: A[4]= 3 cost: 3

3 3 6

4 2 2 1

5 3

6 3 23 6 2 11 6 5 3

Query and Update Comparison (SRPS)

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36 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Original array A

2 1 3 3 6 4 2 1 5 3

2

1 3 3 6

4 2 1

5 3 6 1 3 3 4

3

2 1 5 3

Query: 1+ 2+ 2+ 4= 9 cost: 4 Update: A[4]= 3 cost: 1 SDDC Array

3 1 12 3 6 17 2 8 1 5 3 1 12 3 6 18 3 8 1 5

Query: 17-3-5= 9 cost: 3 Update: A[4]= 3 cost: 2

6 1 12 3 17 2 8 1 5 3

Query and Update Comparison (SDDC)

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SLIDE 37

37 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008 [log2 n] 2[log2 n] Space-Efficient Dynamic Data Cube (SDDC)

  • therwise

4 When n prefect square 4 Space-Efficient Relative Prefix Sum (SRPS) n 2 Prefix Sum (PS) 1 n Original array Note Update cost (worst case) Query cost (worst case) One-dimensional technique

Query-update cost tradeoffs for selected one-dimensional techniques 2 n 2 − n 2

n: size of dimension

Query and Update Comparison

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SLIDE 38

38 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

1 2 4 2log2 n n 1 log2 n

2 2

− n

n

Prefix sum SRPS SDDS Original Cube

One-dimensional array of size n= 16

Query cost Update cost

(Relative position of points can be different for other n)

Query and Update Comparison

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SLIDE 39

39 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Iterative Data Cube (IDC)

Selecting a pre-aggregation method for each

dimension:

The choice of the query-update cost tradeoff depends on the

properties of a dimension.

Example guidelines:

  • If a hierarchy exists for an attribute and users typically query according

to this hierarchy ⇒ Use SDDC or SPRS

  • A dimension has a few values (e.g., gender) ⇒ Use PS

For high-dimensional data cubes one-dimensional

techniques are applied along each dimension.

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40 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

IDC with more then one dimension (example)

Original array IDC array

8 1 6 3 3 2 5 4 3 3 1 2 4 4 5 3 5 1 2 3 3 3 3 3 2 4 2 2 7 8 6 2 3 7 1 4 2 2 1 5 3 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1

PS

(block size 2)

SRPS

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SLIDE 41

41 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

IDC with more then one dimension (example)

Original array IDC array

8 1 6 3 3 2 5 4 3 3 1 2 4 4 5 3 5 1 2 3 3 3 3 3 2 4 2 2 7 8 6 2 3 7 1 4 2 2 1 5 3 5 4 3 2 1 23 15 14 8 5 2 5 17 13 10 7 6 4 4 19 14 11 6 5 3 3 17 14 11 8 6 2 2 33 26 18 12 10 7 1 17 13 11 9 8 3 5 4 3 2 1

PS

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SLIDE 42

42 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

23 15 14 8 5 2 5 17 13 10 7 6 4 4 19 14 11 6 5 3 3 17 14 11 8 6 2 2 33 26 18 12 10 7 1 17 13 11 9 8 3 5 4 3 2 1

Original array

8 1 6 3 3 2 5 4 3 3 1 2 4 4 5 3 5 1 2 3 3 3 3 3 2 4 2 2 7 8 6 2 3 7 1 4 2 2 1 5 3 5 4 3 2 1

SRPS

(block size 2)

PS

23 15 14 8 5 2 5 17 13 10 7 6 4 4 19 14 11 6 5 3 3 17 14 11 8 6 2 2 33 26 18 12 10 7 1 17 13 11 9 8 3 5 4 3 2 1

IDC array

IDC with more then one dimension (example)

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SLIDE 43

43 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

23 15 14 8 5 2 5 17 13 10 7 6 4 4 19 14 11 6 5 3 3 17 14 11 8 6 2 2 33 26 18 12 10 7 1 17 13 11 9 8 3 5 4 3 2 1

Original array IDC array

8 1 6 3 3 2 5 4 3 3 1 2 4 4 5 3 5 1 2 3 3 3 3 3 2 4 2 2 7 8 6 2 3 7 1 4 2 2 1 5 3 5 4 3 2 1

SRPS

(block size 3)

PS

40 28 24 15 11 6 5 17 13 10 7 6 4 4 86 67 51 35 29 15 3 50 40 29 20 16 9 2 33 26 18 12 10 7 1 17 13 11 9 8 3 5 4 3 2 1

IDC with more then one dimension (example)

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SLIDE 44

44 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

A data cube C has 3 dimensions, d1, d2 and d3: d1 d2 d3 d1 size: n, hierarchical attribute -> SDDC d2 size: n hierarchical attribute -> SDDC d3 size: 2 -> PS

IDC C worst case query cost: 2log2n * 2log2n * 2 = 8(log2n)2 worst case update cost: log2n * log2n * 2 = 2(log2n)2

Query and Update Cost of IDC

The worst case update and query costs of a high

dimensional IDC is the product of the worst case costs

  • f all the used one-dimensional techniques.
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SLIDE 45

45 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani 4/14/2008

Conclusion

IDC (Iterative Data Cube)

First pre-aggregation technique on data cube that can take the

specific properties of different dimension attributes into account.

The different dimensions are handled independently.

Features

Development, analysis and implementation are simplified. A greater variety of query-update cost tradeoffs can be generated.