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Flexible Data Cube for Range-Sum Queries in

Dynamic OLAP Data Cubes

Authors: C.-I Lee and Y.-C. LiSpeaker: Y.-C. LiDate :Dec. 19, 2002

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Outline

Introduction Related works Analysis of the average query and

update costs Flexible data cube Performance analysis Conclusions

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Introduction

Data cubes are frequently adopted to implement OLAP and provides aggregate information

Data cube: also known as Multi-dimensional Database(MDDB)

Measure attributes: be chosen as metrics of interest Functional attributes(dimensions):

other attributes of records. Cells: store measure attribute values Range-Sum Query:

add all cells in query region

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Measure attribute → Sale_Volume Dimensions → Year and Age of customers

Car-sales example

5

+

+

4

20

255

1430

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Several previous approaches are used to accelerate the response time

But they slow down the update speed and require further space overhead

This study considers both query and update costs to construct data cubes

No extra space overhead Choice the best cube in any query or update ratio

We also present a FDC method No extra space overhead (for dense data cube) Select or integrate some pre-aggregation

techniques for each dimension

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Related works

The history of pre-aggregate range-sum queries

Prefix Sum(PS)[Ho et al., 1997]

Dynamic Data Cube(DDC)[Geffer et al., 1999b]

Relative Prefix Sum(RPS) [Geffer et al., 1999a]

Hierarchical Cube (HC)[Chan & Ioannidis, 1999]

Double RPS[Liang et al., 2000]

Space-Efficient Data Cube(SEDC)[Riedewal et al., 2000]

Iterative Data Cube(IDC)[Riedewal et al., 2001]

1997 1998 1999 2000 2001

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Prefix Sum(PS) ( Ho et al., 1997 )

3+5+1+2+7+3+2+6+2+4+2+3=40 A: 2+3+3+3+1+5+3+5+1+3+3+4=36 P: 103-50-35+18=36

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Prefix Sum(PS)

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Other methods RPS ( Geffer et al., 1999a)

Two levels(Local PS and overlay boxes) but extra space overhead HC ( Chan & Ioannidis, 1999 )

Hierarchical method DDC ( Geffer et al., 1999b )

Hierarchical method but need extra space overhead SEDC ( Riedewald et al., 2000 )

No exrtra space overhead of RPS and DDC (SRPS and SDDC) Double RPS ( Liang et al., 2000 )

Three levels but need extra space overhead IDC ( Riedewald et al., 2001 )

No extra space overhead (different method in different dimension)

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Our work focuses mainly on methods that do not require any extra space overhead for dense data cubes.

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Analysis of the average query and update costs Assume query ratio + update ratio

=100% Average query cost:

Average update cost: Cu(n) / n

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Flexible Data Cube(FDC)

Exponential time is required to find the optimal pre-aggregated data cube

Proposed the FDC method that is a heuristic method to select or integrate any two pre-aggregation techniques for each dimension.

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In certain situation Size Query ratio

FDCopt = min average cost{FDC candidates}

FDCopt = min{q×CaqFDC + u×CauFDC} Time complexity O(9n)=O(n)

The FDC Method

k’=0 A, LPS or PSk’=1 A, LPS or PSA, LPS or PS

k’=2 A, LPS or PSA, LPS or PS

k’=3 A, LPS or PSA, LPS or PSk’=4 A, LPS or PS

A, LPS or PSk’=5

A, LPS or PS

A, LPS or PSk’=7

A, LPS or PS

A, LPS or PSk’=6 A, LPS

or PS

A, LPS or PS

k’=4 A PS

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Performance analysis

Average cost at different query ratios d = 2, n = 16, 64

0

10

20

30

40

50

60

70

1 0.8 0.6 0.4 0.2 0query ratio (q)

Aver

age

cost

(acc

ess

cells

)

ALPSPSFDC

1

10

100

1000

10000

1 0.8 0.6 0.4 0.2 0

query ratio (q)

Aver

age

cost

(ac

cess

cel

ls)

ALPSPSFDC

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Average cost for different dimension sizes: d = 4, q = 1, 0.9

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

2 4 8 16 32 64 128 256

size (n)

Aver

age

cost

(acc

ess

cells

)

A

LPS

PS

FDC

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

2 4 8 16 32 64 128 256

size (n)

Aver

age

cost

(acc

ess

cells

)

A

LPS

PS

FDC

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Average cost for different dimension sizes: d = 4, q = 0.1, 0

1.E+001.E+011.E+021.E+031.E+04

1.E+051.E+061.E+071.E+081.E+09

2 4 8 16 32 64 128 256

size (n)

Aver

age

cost

(acc

ess

cells

) A

LPS

PS

FDC

1.E+001.E+011.E+021.E+031.E+04

1.E+051.E+061.E+071.E+081.E+09

2 4 8 16 32 64 128 256

size (n)

Aver

age

cost

(acc

ess c

ells)

A

LPS

PS

FDC

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Conclusions

Take both the query and update costs into consideration to select the suitable data cube.

Propose the FDC method select or integrate pre-aggregating techniques for

each dimension. Outperform other methods for any query (or

update) ratio situation linear time: determine the best FDC structure.

In the future, develop new techniques to support sparse data sets

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Thank You