Efficient Top-Down Planning in Business Intelligence

Tobias Lauer • Alexander Haberstroh

Jedox AG

Collaborators: Christoffer Anselm • Zurab Khadikov • Steffen Wittmer

Business Intelligence and Corporate Planning

Jedox Suite

Jedox Suite

Jedox for Excel

Jedox OLAP

Jedox Excel AddIn

Microsoft Excel

SAP Connectivity

Multiprocessor Scalability

Jedox OO-Addin

Open Office Calc

GPU Acceleration

Jedox ETL Data Integration

Data Analysis

Spreadsheet Front-End

Supervision (Events, LDAP)

3rd Party Access (ODBO)

Jedox Web

Jedox Spreadsheet

Jedox Analyzer

Excel2Web

Jedox OLAP Manager

Jedox User Manager

Jedox Report Manager

Jedox ETL Manager

Jedox Mobile

Web Front-End

Mobile Front-End (requires Mobile Server)

iOS App (iPhone, iPad)

Android App

Android widgets

Mobile Server

Online Analytical Processing (OLAP)

• Data modeled as multidimensional “cube”

– Dimensions are structured hierarchically:

• Base elements

• Consolidated elements

– Operations:

• Analysis:

– Multidimensional aggregation (bottom-up)

• Planning:

– Data distribution (top-down)

Jan

Feb

Mar

Q1

Apr

May

Jun

Jul

Q2

Aug

Sep

Q3

Oct

Nov

Dec

Q4

Year

All regions

Europe

France

Italy

UK

North America

USA

Canada

Mexico Deviation

Actual

Budget

Jan Feb Mar Apr May Jun Jul Aug Sep Dec Nov Oct

Q1 Q2 Q3 Q4

Year

Storage model

• Only store base cells with value ≠ 0

• All higher-level (consolidated) cell

values are calculated on demand

when needed

Memory saving, data consistency

Paths and values

Zero and consolidated

values are not stored!

Path compression

Writeback in Top-Down Planning

• Writeback: ”opposite direction”

of aggregation

• Value inserted at high level of

aggregation is broken down to

lower levels until the base

level

• All underlying base cells are

modified, depending on the

type of writeback

Ranges and areas

• Base elements in each dimension are

collected in ranges

D0: { [0,0] , [2,2] } |D0| = 2

D1: { [0,0] , [2,3] } |D1| = 3

D2: { [0,2] } |D2| = 3

• The Cartesian product of ranges

across all dimensions forms an area

D0× D1× D2

Multiply-base distribution

Multiply-base distribution

Set-base distribution

• Every relevant base cell in the area

is set to the same given value

• Naïve approach:

search for all relevant paths and

replace cell values

– Problem: what about zero-value cells,

which are not represented?

• Better approach:

(1) Delete all existing cells in area

(2) Create all cells in area with new

value

Parallel creation of all cell paths in an area

• “Parallel enumeration” of the

area:

– Each thread computes the path of

”its” cell from the thread ID

– Problem:

• Gaps between ranges of a

dimension prevent simple iterations

• Iterating over all ranges and counting

all visited elements is inefficient

– Solution:

• Represent ranges by pre-calculated

prefix sums (rather than start and

end points)

Prefix sum representation of ranges

(1) Find smallest m such that r[m] ≥ k

(2) i = g[m] + k

Prefix sums of gap lengths: g =

Prefix sums of range lengths: r =

Index i of kth relevant element in D:

Add-base distribution

• The same given value v is added

to the value of each relevant base

cell

• Approach:

– Create all cells of the area and set

value to v (as before) and store them

temporarily

– Find all previously existing relevant

cells and add their (old) value to the

one in the new temporary area

– Delete old relevant cells and persist

temporary storage

Performance tests Timings

(in ms)

CPU

Intel DualCore

2x GPU

GeForce 260

3x GPU

Tesla C1060

4x GPU

Tesla C2050

Multiply-base 1 3,548 466 (7.6 x) 558 (6.4 x) 435 (8.2 x)

Refresh 1 1,131 200 (5.7 x) 127 (8.9 x) 74 (15.3 x)

Sum 4,679 666 (7.0 x) 685 (6.8 x) 509 (9.2 x)

Multiply-base 2 21,542 513 (42 x) 580 (37 x) 448 (48 x)

Refresh 2 5,508 961 (5.7 x) 617 (8.9 x) 347 (16 x)

Sum 27,050 1,474 (18 x) 1,197 (23 x) 795 (34 x)

Timings (in ms)

CPU

Intel DualCore

2x GPU

GeForce 260

3x GPU

Tesla C1060

4x GPU

Tesla C2050

Set-base 14,979 900 (17 x) 715 (21 x) 572 (26 x)

Refresh 5,598 962 (5.8 x) 610 (9.2 x) 347 (16 x)

Sum 20,577 1,862 (11 x) 1,325 (16 x) 919 (22 x)

Timings (in ms)

CPU

Intel DualCore

2x GPU

GeForce 260

3x GPU

Tesla C1060

4x GPU

Tesla C2050

Add-base 110,387 1,465 (75 x) 899 (123 x) 872 (127 x)

Refresh 5,621 953 (5.9 x) 608 (9 x) 346 (16 x)

Sum 116,008 2,418 (48 x) 1,507 (77 x) 1,218 (95 x)

Speed-up factors (compared to CPU)

2x GeForce 260

3x Tesla C1060

4x Tesla C2050

0

20

40

60

80

100

7x

11x

18x

48x

7x

16x

23x

77x

9x

22x

34x

95x

Add-base Multiply-base 2

Multiply-base 1 Set-base

Concluding remarks

• Top-down planning creates and/or manipulates large numbers of data

records

– These updates are systematic and structured

– GPUs are well-suited for parallel execution

– CUDA implementation shows nice speedup compared to sequential CPU algorithm

– Can benefit from multiple GPUs

• Approach commercially implemented in Jedox Suite

Contact

www.jedox.com

• Alexander Haberstroh alexander.haberstroh@jedox.com

• Tobias Lauer tobias.lauer@jedox.com

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

16 0 3 24 10 0 21 35

4 13 29 0 31 17 16 0

67 0 24 8 0 13 8 13

0 0 0 0 0 0 0 0

51 5 27 39 73 44 12 46

19 0 3 86 54 0 6 0

0 49 0 0 13 90 0 28

0 42 11

0 2 0

0 81 54

0 0 0

0 33 1

0 92 0

0 0 60

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

Multiply-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

240

Multiply-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

240

Multiply-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

240

x2

Multiply-base distribution

16 3 24 10 21 35

4 26 58 31 17 32

67 48 16 13 16 26

51 10 54 78 73 44 24 92

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

480

Multiply-base distribution

16 3 24 10 21 35

4 26 58 31 17 32

67 48 16 13 16 26

51 10 54 78 73 44 24 92

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

480

Set-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

B 10

Set-base distribution

16 3 24 10 21 35

4 10 10 10 31 17 10 10

67 10 10 10 13 10 10

10 10 10 10 10

51 10 10 10 73 44 10 10

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

B 10

Set-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

10 10 10 10 10

10 10 10 10 10

10 10 10 10 10

10 10 10 10 10

Set-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

10 10 10 10 10

10 10 10 10 10

10 10 10 10 10

10 10 10 10 10

Set-base distribution

16 3 24 10 21 35

4 31 17

67 13

51 73 44

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

10 10 10 10 10

10 10 10 10 10

10 10 10 10 10

10 10 10 10 10

Set-base distribution

16 3 24 10 21 35

4 10 10 10 31 17 10 10

67 10 10 10 13 10 10

10 10 10 10 10

51 10 10 10 73 44 10 10

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

Add-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

B+5

Add-base distribution

16 3 24 10 21 35

4 13

+5

29

+5 +5 31 17

16

+5 +5

67 +5 24

+5

8

+5 13

8

+5

13

+5

+5 +5 +5 +5 +5

51 5

+5

27

+5

39

+5 73 44

12

+5

46

+5

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

B+5

Add-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

5 5 5 5 5

5 5 5 5 5

5 5 5 5 5

5 5 5 5 5

Add-base distribution

16 3 24 10 21 35

4 13 29 31 17 16

67 24 8 13 8 13

51 5 27 39 73 44 12 46

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

18 34 5 21 5

5 29 13 13 18

5 5 5 5 5

10 32 44 17 51

Add-base distribution

16 3 24 10 21 35

4 31 17

67 13

51 73 44

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

18 34 5 21 5

5 29 13 13 18

5 5 5 5 5

10 32 44 17 51

Add-base distribution

16 3 24 10 21 35

4 18 34 5 31 17 21 5

67 5 29 13 13 13 18

5 5 5 5 5

51 10 32 44 73 44 17 51

19 3 86 54 6

49 13 90 28

42 11

2

81 54

33 1

92

60

340